$MathMaster logo$

MathMaster

Home
general
a bus averages 2miles per hour faster than a motorcycle if the bus travels 165miles in the same time it takes the motorcyc

Question

A bus averages. 2miles per hour faster than a motorcycle. If the bus travels 165miles in the same time it takes the motorcycle to travel 155miles, then what is the speed of each?

53

likes

266 views

Answer to a math question A bus averages. 2miles per hour faster than a motorcycle. If the bus travels 165miles in the same time it takes the motorcycle to travel 155miles, then what is the speed of each?

$Expert avatar$

4.7

86 Answers

1. Let

v_m

be the speed of the motorcycle in miles per hour.
2. The speed of the bus is therefore

v_b = v_m + 2

miles per hour.
3. The time it takes for the motorcycle to travel 155 miles is

\frac{155}{v_m}

hours.
4. The time it takes for the bus to travel 165 miles is

\frac{165}{v_b}

hours.

Since these times are equal:

\frac{155}{v_m} = \frac{165}{v_b}

5. Substitute

v_b = v_m + 2

into the equation:

\frac{155}{v_m} = \frac{165}{v_m + 2}

6. Cross-multiply to solve for

v_m

:

155(v_m + 2) = 165v_m

155v_m + 310 = 165v_m

310 = 10v_m

v_m = 31

7. Therefore, the speed of the motorcycle is

v_m = 31

mph.
8. The speed of the bus is:

v_b = v_m + 2 = 31 + 2 = 33

mph

Answer:

v_m = 31 \text{ mph}, \quad v_b = 33 \text{ mph}

Frequently asked questions (FAQs)

What are all the possible values of the major and minor axes lengths of an ellipse, given its foci and sum of distances to the foci?

+

What is the volume of a rectangular solid with length 5cm, width 8cm, and height 12cm?

+

What is the factored form of 12x^2 - 16x + 4?

+

New questions in Mathematics

Find two natural numbers whose sum is 230 and their difference is 10. Set up the system and solve it.

90 divided by 40

Two events E and F are ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.

The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places

Convert 78 percent to a decimal

form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?

Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.

TEST 123123+1236ttttt

cube root of 56

Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)

find missing measure for triangle area = 48 m square base = 10m heaighy = ? m

Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?

Below are three 95% CIs (where 𝜎 was known and 𝑥̅happened to be the same); one with sample size 30, one with samplesize 40, and one with sample size 50. Which is which?(66.2, 76.2)(61.2, 81.2)(56.2, 86.2)

Evaluate ab+dc if a=56 , b=−34 , c=0.4 , and d=12 . Write in simplest form.

22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.

Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?

Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.