Question

During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph?

Answer 1

Remember that distance equals rate multiplied by time, or put more compactly, $d=rt$

Here, we're looking for the distance traveled by a truck, given only its rate, 44 mph. We're also given that both of the vehicles travel for is the same. This lets us use the car's information to find that time, which we can then use to find the distance traveled by the truck.

For the car, our distance is 120 miles, our rate is 55 mph, and our time is unknown; let's call that value $t$. We have:

$120=55t$

Dividing both sides by 55, we find:

$\frac{120}{55}=t\\\\ \frac{24}{11}=t$

So our time is 24/11 hours - roughly 2 hours and 13 minutes. We'll use the 24/11 value to get as exact an answer as we can, though.

For the truck, we know its rate and its time (24/11 hours), but we don't know its distance. We'll call it $d$. Putting in our new value for time, we have:

$d=44 \big(\frac{24}{11}\big) \\ d=4(24)\\ d=96$

So, in 24/11 hours, the truck will have traveled 96 miles traveling at its average speed.