Question

A small plane travels 90 mph faster than a train. The plane travels 525 miles in the same time it takes the train to travel 210 miles. Determine the rate of each.

A) Plane: 105 mph, Train: 15 mph
B) Plane: 120 mph, Train: 30 mph
C) Plane: 150 mph, Train: 60 mph
D) Plane: 180 mph, Train: 90 mph

Answer 1

The rate of the plane is 105 mph and the rate of the train is 15 mph.

Step-by-step explanation:

Let's assume the rate of the train is x mph. Since the plane travels 90 mph faster than the train, the rate of the plane is (x + 90) mph.

We can use the formula distance = rate × time to solve this problem. Let the time taken by both the plane and the train be t hours.

For the plane, the distance is 525 miles and the rate is (x + 90) mph. So we have the equation 525 = (x + 90) × t.

For the train, the distance is 210 miles and the rate is x mph. So we have the equation 210 = x × t.

We can solve these two equations simultaneously to find the values of x and t, which will give us the rates of the plane and the train.

A) Plane: 105 mph, Train: 15 mph