Question

Question 3

Jane spent 2 hours exploring a mountain with a dirt bike. When she rode the 40 miles uphill, she went 5 mph slower than
when she reached the peak and rode for 12 miles along the summit. What was her rate along the summit?

Answer 1

30 mph was the rate she was going

Answer 2

30 mph

Explanation:

time = distance/speed

If x represents Jane's speed along the summit then her total exploration time is ...

12/x + 40/(x -5) = 2 . . . . . hours

Multiplying by (x)(x -5), we get ...

12(x -5) +40(x) = 2(x)(x -5)

Dividing by 2 and subtracting the left side gives ...

x^2 -31x +30 = 0

(x -30)(x -1) = 0 . . . . . factor

Solutions are x = 30 and x = 1, values of x that make the factors zero. A speed of 1 mph makes no sense in this problem, so ...

Jane's speed along the summit was 30 mph.