Question

The plane could go 6 times as fast as the car. Thus the plane could go 1200 miles in only one hour less than it took the car to go 250 miles. Find the rate and time of the car and rate and time of the plane

Answer 1

Answer:

The speed of the car is 50 mph and that of the plane is 300 mph.

Time taken by the car is 5 hours and that taken by the plane is 4 hours.

Step-by-step explanation:

Let the speed of the car is u mph and that of the plane is v mph.

So, v = 6u ............ (1)

Now, as per the given condition, we can write the equation as

$\frac{1200}{v} + 1 = \frac{250}{u}$

⇒ $\frac{1200}{6u} + 1 = \frac{250}{u}$ {From the equation (1)}

⇒ $\frac{250}{u} - \frac{200}{u} = 1$

⇒ $\frac{50}{u} = 1$

⇒ u = 50 mph.

So, v = 6 × 50 = 300 mph.

And, the time taken by the car is $\frac{250}{50} = 5$ hours and that taken by the plane is (5 - 1) = 4 hours. (Answer)