Can't figure out

Question

Clint and Jim rode their bicycles to centennial park at an average of 8mi/hr. It took them 1 hour longer to return home riding at an average of 7mi/hr on a route that was 4 miles longer than their route there. how long were they riding their bicycle? How many miles did they ride each way? 

Answer 1

 

how long were they riding their bicycle? How many miles did they ride each way?

Let

D = Distance (mi)

t = time (hr)

 

The route there:

 

8mi/hr (t) = D

The route back:

 

7mi/hr (t+1hr) = D + 4mi

 

Substitute the first Eq. in for D in the second Eq.

 

7mi/hr (t+1hr) = (8mi/hr (t)) + 4mi

Units cancel out, giving t in hr.   

7(t+1) = 8t + 4

 

Solve for t

7(t+1) = 8t + 4

7t + 7 = 8t + 4

7 - 4 = 8t - 7t

3 = t

It takes them 3 hrs to ride there and 4 hrs to ride back (problem states 1 hr longer)

Use t= 3 to find the distance traveled there and add on the 4mi to find the distance back.

8mi/hr (t) = D

8mi/hr (3hr) = 24 mi there

24 mi + 4 mi = 28 mi back