A train can travel 280 miles in the same time that it takes a car to travel 140 miles. If the train's rate is 40 miles per hour faster than the cars, find the average for each.
Distance D = Rate R * Time T
T = D/R
R = rate for car
R + 40 = rate for train
140/R = time for car
280/(R + 40) = time for train
Times are equal
280/(R + 40) = 140/R
Cross multiply and solve for R, rate for car
R + 40 = rate for train
80
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume the speed of the car is 'x' miles per hour. According to the problem, the train's speed is 40 miles per hour faster than the car's speed, so the train's speed would be 'x + 40' miles per hour.
Now, using the formula mentioned above, we can calculate the time taken by the train and the car.
Time taken by the train = Distance / Train's Speed
Time taken by the car = Distance / Car's Speed
Given that the train can travel 280 miles in the same time it takes the car to travel 140 miles, we can set up the equation:
280 / (x + 40) = 140 / x
To solve for x, we can cross multiply:
280x = 140(x + 40)
280x = 140x + 5600
Subtracting 140x from both sides:
140x = 5600
Dividing both sides by 140:
x = 40
Therefore, the speed of the car is 40 miles per hour.
Plugging this back into the equation for the train's speed:
Train's speed = Car's speed + 40
Train's speed = 40 + 40 = 80 miles per hour
Hence, the average speed of the car is 40 miles per hour, and the average speed of the train is 80 miles per hour.