MathMaster logo

MathMaster

  1. Home
  2. general
  3. 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
Madelyn
4.7
88 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 is the value of log(base 5)36?
+
Question: What is the volume of a cube with side length 's' and surface area 'A'?
+
What is the perimeter of a rectangle with length 10 and width 15?
+
New questions in Mathematics
Solution of the equation y'' - y' -6y = 0
Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) &lt;2u- 5v,3w&gt;
A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?
two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?
You have been hired to estimate the average weight of quarters in circulation. Based on the sample of quarters you collect (below), create a 90% confidence interval for the weight of quarters in circulation. Quarter Weights (grams) 5.631 5.714 5.719 5.689 5.551 5.723 5.705 5.627 5.627 5.715 5.576 5.632 5.641 5.676 5.660 5.699 5.609 5.634 5.713 5.591 5.674 5.675 5.684 5.694 5.655 5.632 5.598 5.675 5.628 5.562 5.636 5.583 5.567 5.551 5.649 5.708 5.696 5.614 5.637 5.601 5.628 5.711 5.566 5.653 5.653 5.597 5.687 5.717 5.678 5.654 5.556 5.707 5.563 5.628 5.679 5.714 5.555 5.719 5.634 5.647 5.717 5.612 5.705 5.657 5.670 5.607 5.687 5.666 5.612 5.718 5.714 5.713 5.663 5.641 5.589 5.656 5.712 5.639 5.577 5.580 5.674 5.636 5.625 5.597 5.616 5.591 5.616 5.700 5.706 5.695 5.562 5.699 5.607 5.573 5.659 5.632 5.654 5.568 5.628 5.687 5.605 5.689 5.687 5.554 5.618 5.701 5.681 5.645 5.714 5.665 5.661 5.634 5.714 5.586 5.656 5.673 5.657 5.717 5.611 5.578 5.579 5.614 5.644 5.724 5.647 5.566 5.697 5.558 5.586 5.586 5.611 5.573 5.573 5.709 5.629 5.649 5.552 5.615 5.645 5.611 5.686 5.588 5.641 5.704 5.703 5.696 5.557 5.551 5.725 5.608 5.725 5.603 5.677 5.638 5.573 5.640 5.561 5.631 5.563 5.671 5.662 5.569 5.648 5.680 5.681 5.551 5.555 5.578 5.701 5.645 5.670 5.574 5.594 5.705 5.633 5.719 5.680 5.647 5.641 5.553 5.616 5.698 5.552 5.566 5.559 5.697 5.686 5.560 5.629 5.701 5.622 5.615 5.553 5.608 5.637 5.663 5.696 5.714 5.675 5.613 5.594 5.669 5.569 5.716 5.705 5.603 5.709 5.717 5.606 5.581 5.575 5.601 5.600 5.664 5.715 5.705 5.583 5.586 5.592 5.550 5.628 5.662 5.603 5.559 5.676 5.558 5.678 5.671 5.642 5.581 5.568 5.706 5.665 5.712 5.574 5.602 5.699 5.716 5.693 5.711 5.635 5.612 BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)*** BLANK #2: What is the LOW end of the estimate ***ANSWER TO 3 DECIMALS*** BLANK #3: What is the HIGH end of the estimate ***ANSWER TO 3 DECIMALS***
Estimate the fifth term if the first term is 8 and the common ratio is -1/2
4. Show that if n is any integer, then n^2 3n 5 is an odd integer
Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)
12(3+7)-5
3+7
The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .
3%2B2
Show work on 4108 divided by 4
(6Β²-14)Γ·11β€’(-3)
On Tuesday Shanice bought five hats.On Wednesday half of all the hats that she had were destroyed.On Thursday there were only 17 left.How many Did she have on Monday.
Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DGβŠ₯BG. If the area of the quadrilateral AGBD is equal to s, show that ACΒ·BDβ‰₯2Β·s.
The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.
2 - 6x = -16x + 28
1. The cost to transport 250 packages of cement 120 kilometers is $600. What will be the cost to transport 500 packages 300 kilometers?
A membership to the gym cost $25 per person in 1995. The membership cost has increased by an average $6 per person for each year since 1995. Write a linear equation for the cost of a gym membership for one person since 1995. What is the cost of a gym membership in 2009?

You might be interested in