Question

Rob’s tractor is just as fast as Lucy’s. It takes Rob 1 hour more than it takes Lucy to drive to town. If Rob is 42 miles from town and Lucy is 28 miles from town, how long does it take Lucy to drive to town?

Answer 1

Rob:

42 miles

time = x + 1 h

rate = 42 / (x+1) mph

Lucy:

28 miles

time = x h

rate = 28 / x mph

equation is

rate = rate

$\begin{gathered} \frac{42}{x+1}=\frac{28}{x} \\ 42x=\frac{28}{x}(x+1) \\ 42x=28x+28 \\ 42x-28x=28x+28-28x \\ 14x=28 \\ \frac{14x}{14}=\frac{28}{14} \\ x=2 \end{gathered}$

time for Lucy to drive to town is 2 h