MathMaster logo

MathMaster

  1. Home
  2. general
  3. a person travels by car from one city to another with different constant speeds between pairs of cities she drives for 55
Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.

177

likes
886 views

Answer to a math question A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.

Expert avatar
Seamus
4.9
98 Answers
To find the average speed for the trip, we need to divide the total distance traveled by the total time taken.

First, we need to calculate the distance traveled during each leg of the trip.

For the first leg, the person drives for 55.0 minutes at 100.0 km/h. We can calculate the distance as follows:

Distance = Speed * Time
Distance = 100.0 km/h * (55.0 min / 60 min) [converting minutes to hours]
Distance = 91.7 km

For the second leg, the person drives for 14.0 minutes at 65.0 km/h. Again, we can calculate the distance:

Distance = Speed * Time
Distance = 65.0 km/h * (14.0 min / 60 min) [converting minutes to hours]
Distance = 15.8 km

For the third leg, the person drives for 45.0 minutes at 60.0 km/h. Calculating the distance:

Distance = Speed * Time
Distance = 60.0 km/h * (45.0 min / 60 min) [converting minutes to hours]
Distance = 45.0 km

Now, let's calculate the total distance:

Total Distance = Distance of first leg + Distance of second leg + Distance of third leg
Total Distance = 91.7 km + 15.8 km + 45.0 km
Total Distance = 152.5 km

Next, we need to calculate the total time taken:

Total Time = Time for first leg + Time for second leg + Time for third leg + Time for lunch and gas
Total Time = 55.0 min + 14.0 min + 45.0 min + 20.0 min
Total Time = 134.0 min

Finally, we can find the average speed by dividing the total distance by the total time:

Average Speed = Total Distance / Total Time
Average Speed = 152.5 km / (134.0 min / 60 min) [converting minutes to hours]
Average Speed = 68.21 km/h

Therefore, the average speed for the trip is 68.21 km/h.

\boxed{68.21 \, \text{km/h}}

Frequently asked questions (FAQs)
What is the volume of a rectangular solid with length (l), width (w), and height (h), given by the formula V = l * w * h?
+
Find the measure of angle C in triangle ABC given that angle A measures 40 degrees and angle B measures 70 degrees.
+
What is the axis of symmetry of the parabola represented by the function y = -2x^2 + 3x - 5?
+
New questions in Mathematics
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?
3(4×-1)-2(×+3)=7(×-1)+2
The profit G of the company CHUNCHES SA is given by G(x) = 3×(40 – ×), where × is the quantity of items sold. Find the maximum profit.
6. Among 100 of products there are 20 rejects. We will randomly select 10 of products. The random variable X indicates the number of rejects among the selected products. Determine its distribution.
4X^2 25
(-5/6)-(-5/4)
Subscribers to the FAME magazine revealed the following preferences for three categories: Fashion 30, Athletics 24 and Business 15. Following these frequencies of observation, compute the chi-square test statistic. At the 0.05 level of significance, would you conclude they are similar?
I need to know what 20% or £3292.75
7. Find the equation of the line passing through the points (−4,−2) 𝑎𝑛𝑑 (3,6), give the equation in the form 𝑎𝑥+𝑏𝑦+𝑐=0, where 𝑎,𝑏,𝑐 are whole numbers and 𝑎>0.
Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4336 patients treated with the​ drug, 194 developed the adverse reaction of nausea. Construct a ​99% confidence interval for the proportion of adverse reactions.
Sabendo+que+o+tri%C3%A2ngulo+ABC+%C3%A9+ret%C3%A2ngulo+e+que+um+de+seus+%C3%A2ngulos+mede+30+quanto+mede+o+terceiro+ tri%C3%A2ngulo
In measuring the internal radius of a circular sewer the measurement is 2% too large. If this measurement is then used to calculate the circular cross-sectional area of the pipe: Determine, by using the binomial theory, the percentage error that will occur compared to the true area.
In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1
48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?
Given the word WEIRD, determine a four-letter offspring that can be formed with the letters of the word written above
Find sup { x∈R, x²+3<4x }. Justify the answer
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water. a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water? b) What magnitude of thrust does the ingot receive when it is submerged? c) What would the weight of the ingot have to be when it is submerged? Data Pagua = 1000 kg/m³ Pagua= 19300 kg/m³
An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?

You might be interested in