Question

An express train and car leave Los Angeles at the same time and head for Merced 280 miles away. The rate of the train is twice the rate of the car. The train arrives 4 hour before the car arrives. Find the rate of the car.

Answer 1

Now, recall your d = rt, or distance = rate * time

so.. the train and the car, both leave LA, and go to Merced, which is 280miles away.....alrite, the train is going twice as fast as the car is, so, if the car is going "r" fast, then the train is going 2*r or 2r fast

now, the train arrives 4hrs earlier than the car, so, if the car took "t" time to arrive, the train took then t-4

now, both, arrived at Merced, that means, the distance covered by each, is 280miles

thus      $\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ train&280&2r&t-4\\ car&280&r&t \end{array} \\\\\\ \begin{cases} 280=2r(t-4)\\\\ 280=rt\implies \cfrac{280}{r}=\boxed{t}\\ ----------\\ 280=2r\left( \boxed{\cfrac{280}{r}}-4 \right) \end{cases}$

solve for "r"