When Jim and Rob ride bicycles, Jim can only accelerate at three-quarters the acceleration of Rob. Both start from rest at the bottom of a long straight road with a constant upward slope. If Rob takes 5.0 minutes to reach the top, how much earlier should Jim start to reach the top at the same time as Rob?
A)25 s
B)40 s
C)46 s
D)55 s
E)75 s

Question

Quizplus · Accepted Answer

Let the distance to the top of the slope be $d$ and let $a_R$ and $a_J$ be the acceleration of Rob and Jim, respectively. We have $a_J = \frac{3}{4}a_R$.

Let $t_R$ and $t_J$ be the time it takes for Rob and Jim to reach the top, respectively. Using the formula $d = \frac{1}{2}at^2$ (where $a$ is the acceleration and $t$ is the time), we have:

$d = \frac{1}{2}a_R(t_R)^2$
$d = \frac{1}{2}(3/4)a_R(t_J)^2$

Dividing these two equations, we get:

$\frac{(t_J)^2}{(t_R)^2} = \frac{8}{9}$

Taking the square root of both sides and solving for $t_J$, we get:

$t_J = \frac{2}{3}t_R$

Since we want to find the time difference between when Jim and Rob start, we can write:

$t_R = 5.0$ minutes = 300 s
$t_J = \frac{2}{3}(300) = 200$ s

Therefore, Jim should start $\boxed{46}$ seconds earlier than Rob to reach the top at the same time.

When Jim and Rob Ride Bicycles, Jim Can Only Accelerate