Please help me find the rate. Detailed explanation please.

Question

A car and a bus set out at 2 P.M. from the same point headed in the same direction. The average speed of the car is twice the average speed of the bus. In 2 h, the car is 68 mi ahead of the bus. Find the rate of the car.

Answer 1

So let's start by figuring out what how far the car has gone in 2 hours. We are told that it is 68 miles ahead of the bus at this point and that the car is traveling at twice the speed of the bus. Given this information we can reason that the car has gone a total of 136 miles in those 2 hours.* To figure out the rate in miles per hour we simply divide the miles traveled (136) by the hours lapsed (2) which gives us a value of 68 in units of miles per hour.

Let me know if this makes sense!

*To visualize the total distance traveled by the car after 2 hours it is best to think of the bus as being at the halfway point between the car and the starting point for both vehicles.

Answer 2

Hello, Madison. Okay, well the equation you need to use is Distance = rate x time

Let's let r = the speed of the bus

then, as stated, the speed of the car is 2 x r or 2r

so, at 2 hours, the distance of the bus is r x 2 hours or 2r

Also, at 2 hours the distance of the car is 2(2r) = 4r

It also says that at 2 hours the distance of the car is 68 more than the bus.

So we can now show our equation:

4r = 2r + 68

Now, solve:

4r - 2r = 2r - 2r +68

2r = 68

r = 34

So, the speed of the bus is 34 mph

Therefore, the speed of the car is 2r = 68 mph