Tina is training for a biathlon To train for the running por

Tina is training for a biathlon. To train for the running portion of the race, she runs 8 miles each day over the same course. The first 2 miles of the course is on level ground, while the last 6 miles is downhill. She runs 3 mph slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course?

Solution

Let speed at downhill =x mph

then

speed on ground = (x-3) mph

Thus use formula time=speed/distance,

(Time taken to travel 2 miles on ground) +(Time taken to travel 6 miles on downhill) = 1

2/(x-3) + 6/x =1

Multiply both sides by x(x-3)

2x+6(x-3)=x(x-3)

8x-18=x^2-3x

x^2-11x+18=0

(x-9)(x-2)=0

x=9,2

Discard the value x=2, as speed on ground will become negative.

Thus, speed on downhill is 9 mph