Maths 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

This problem has more information than you really need to solve it. Begin by creating a formula that represents each situation. Because there are two unknowns for which to solve, you will need only two formulas.

 

1) t1 x 4km/h + t2 x 7km/h = 26km (original situation)

 

2) t1 x 4km/h + t1 x 7km/h = 29km (from the "If he had run for the same time..." sentence)

 

From the latter formula, you can solve for t1, right?

 

t1 x (4km/h + 7km/h) = 29km

t1 = 29km / 11 km/h = 29/11 h

 

"Plug that" back into the original situation and solve for t2.

 

1) 29/11 x 4km/h + t2 x 7km/h = 26km

 

Once you've solved that, the total time will be t1 + t2 (obviously).

 

HINT: The correct answer is between four and five hours.