Trevor can bike 35 mi in the same time that it takes him to

Trevor can bike 35 mi in the same time that it takes him to hike 7.5 mi. If he bikes 11 mph faster than he hikes, find his rates for biking and hiking.

Solution

Let his rate of biking be x

Let his rate of hiking be y

Trevor can bike 35 mi in the same time that it takes him to hike 7.5 mi:

35/x = 7.5/y -----(1)

35y -7.5x =0

he bikes 11 mph faster than he hikes

x -y = 11 -----(2)

solve the two equations to get the values of x and y:

Multipley equ (2) by 35 and then add both equation:

we get y = 3 ; x= 14

So, he bikes with 14 mi/hr and hikes with 3 mi/hr