word problem

Question

Suppose that a cyclist began a
578
mi ride across a state at the western edge of the? state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after
8.5
hr and the car traveled
34.2
mph faster than the? bicycle, find the average rate of each.

Answer 1

Hi Amy,

 

Let's see what we have and what we need to find.

 

First of all, this is a distance, rate, time problem

d = rt

 

We know the distance is 578 miles

We know the total time traveled was 8.5 hours

We know the cars traveled 34.2 mph faster than the bike

 

So let

r_b be the speed of the bike

r_c is the speed of the car

r_c = r_b + 34.2

 

8.5r_c + 8.5 r_b = 578

Since rc = r_b + 34.2

 

8.5 (r_b+34.2) + 8.5r_b = 578

distribute and combine terms

 

8.5r_b + 290.7 + 8.5r_b = 578

17r_b + 290.7 = 578

17r_b = 287.3

r_b = 16.9

 

r_c = r_b + 34.2

r_c = 16.9 + 34.2

r_c = 51.1

 

The bicycle travels at an average speed of 16.9 mph.

The car travels at an average speed of 51.1 mph.