Algebra Word Problem

Question

Stevie biked 96 miles in a day. She split the ride into two parts, before and after lunch. Before lunch she biked 42 miles. The amount of time she spent riding after lunch was 1 hour more than the amount of time she spent riding before lunch. Her average speed was the same for both parts of the ride. Find the amount of time in hours she spent riding after lunch.

Answer 1

Let t = time after lunch, and t-1 = time before lunch.

 

Since she rode 96 miles for the total time, and 42 miles before lunch, she rode 96-42 or 54 miles after lunch.

 

remember that distance equals rate times time, and therefore, r = d/t and the rates before and after lunch were the same, 42/(t-1) = 54/t.

 

If we multiply by t(t-1) on each side, we get 42t = 54(t-1) or 42t = 54t-54.

 

Solving this equation we get t = 54/12 = 9/2 or 4.5 hours.