Uniform Motion

Question

A commuter bus takes 2 hours to get downtown; an express bus,averaging 25 mph faster, takes 45 minutes to cover the same route, What is the average speed for the commuter bus?

Answer 1

Use the formula:

                                 total distance = average speed x total time  (1)

Let's use the variables: v₁ - averafe speed for a commuter bus

                                  v₂ - average speed for an express bus

Given:    t₁ = 2 h, t₂= 45 min = 0.75 h, v₂ = v₁ + 25 mph

    According to fomula (1) we can write the following equation:

                                       2v₁ = 0.75 v₂ = (v₁ + 25) 0.75

If you solve the equation for v₁ you will obtain: v₁ = 18.75 miles/1.25 h = 15mph.

                                                Answer: v₁ = 15mph

Comment: if you are given the same physical quantity (time) in two different units (hours and minutes) you have to convert them to the same units. In this case is better to use time in hours. Thus, for the second bus you will get speed = 40 mph and the total distance traveled = 30 miles.