Question

A bus traveled on a level road for 4 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 5 hours. Find the average speed on the level road if the entire trip was 449 miles.

Answer 1

To solve this problem, we must recall that the formula for velocity assuming linear motion:

v = d / t

Where,

v = velocity

d = distance

t = time

 

For condition 1: bus travelling on a level road

v1 = d1 / t1

(v2 + 20) = (449 – d2) / 4                        --->1

 

For condition 2: bus travelling on a winding road

v2 = d2 / t2

v2 = d2 / 5                                            --->2

 

Combining equations 1 and 2:

(d2 / 5) + 20 = (449 – d2) / 4

0.8 d2 + 80 = 449 – d2

1.8 d2 = 369

d2 = 205 miles

 

Using equation 2, find for v2:

v2 = 205 / 5

v2 = 41 mph

 

Since v1 = v2 + 20

v1 = 41 + 20

v1 = 61 mph

 

Therefore the average speed on the level road is 61 mph.