Question

Jane spent 3 hours exploring a mountain with a dirt bike. First, she rode 48 miles uphill. After she reached the peak she rode for 15 miles along the summit. While going uphill, she went 5 mph slower than when she was on the summit. What was her rate along the summit?

Answer 1

Answer: $25\ mph$

Step-by-step explanation:

Given

Jane took 3 hours

First she rode 48 miles with let say with $x$ mph

then she rode 15 miles with speed $(x+5)$ mph

Equate the time in each ride and equate it to total time

$\Rightarrow 3=\dfrac{48}{x}+\dfrac{15}{x+5}\\\\\Rightarrow 3x(x+5)=48(x+5)+15x\\\\\Rightarrow 3x^2+15x=48x+48\times 5+15x\\\\\Rightarrow 3x^2-48x-240=0\\\\\Rightarrow (x-20)(x+4)=0\\\\\text{Neglecting the negative value as speed cannot be negative}\\\\\Rightarrow x=20\ mph$

So, her along the summit is $x+5=25\ mph$