Word problem

Question

A fitness fanatic walks at 4 km/h for time t1, and then runs at 7 km/h for time t2. He travels a total of 26 km. If he had run for the same time that he had walked (t1) and walked for the same time that he had run (t2), then he would have travelled 29 km. What was the total time spent walking and running?

Answer 1

Distance = Rate times Time, or D = R*T

 

4*T1 + 7*T2 = 26  from the 1st 2 sentences

7*T1 + 4*T2 = 29  from the "If he had ..." sentence 

 

Multiply the 1st equation by (-7) and the 2nd equation by 4 and then add the 2 equations together 

 

-28*T1 - 49*T2 = -182

28*T1 + 16*T2 = 116 

 

-33*T2 = -66

T2 = 2 

 

Plug this value in to the 1st equation to solve for T1 

 

4*T1 + 7*(2) = 26

4*T1 + 14 = 26

4*T1 = 12

T1 = 3 

 

So he walked for 3 hours and ran for 2 hours 

 

Check:  (4 km/h)*(3 h) + (7 km/h)*(2 h) = 12 km + 14 km = 26 km 

            (7 km/h)*(3 h) + (4 km/h)*(2 h) = 21 km + 8 km = 29 km