A truck can travel 210 miles in the same time it takes a car to travel 350 miles. If the trucks rate is 20 miles per hour slower than the car's, find the average rate for each.

The speed of the truck is 30 mph.

The speed of the car is 50 mph.

Step-by-step explanation:

Let x represent the speed of the car. If the trucks rate is 20 miles per hour slower than the car's, it means that the speed of the truck is

(x - 20) miles per hour.

Time = distance/speed

The truck can travel 210 miles in the same time it takes the car to travel 350 miles. It means that the time it would take the truck to travel 210 miles is

210/(x - 20)

Also, the time it would take the car to travel 350 miles is

350/x

Since the time is the same, it means that

210/(x - 20) = 350/x

Cross multiplying, it becomes

350(x - 20) = 210x

350x - 7000 = 210x

350x - 210x = 7000

140x = 7000

x = 7000/140

x = 50

The speed of the truck is

x - 20 = 50 - 20 = 30 mph

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