JASON DRIVES 50 MI TO A TRAIN and then continues his trip with a 210 mi train ride. the car travels 20 mph slower than the train. if total travel time is 4 hr, find the average speed of the car and the average speed of the train.
To find the average speed of the car and the train, we need to break down the journey into two parts: the distance traveled by the car and the distance traveled by the train.
Let's first find out the speed of the train.
Let the speed of the train be 's' mph. We are given that the total travel time is 4 hours.
Jason drives 50 miles to reach the train. The time taken for this part of the journey can be found by dividing the distance by the speed of the car.
Time taken = Distance / Speed
Time taken = 50 miles / (s - 20 mph)
The train ride is 210 miles long. The time taken for this part of the journey can be found by dividing the distance by the speed of the train.
Time taken = Distance / Speed
Time taken = 210 miles / s mph
Since the total travel time is 4 hours, we can write the equation:
Time taken by car + Time taken by train = Total travel time
(50 / (s - 20)) + (210 / s) = 4
Now we can solve this equation to find the value of 's' which represents the speed of the train.
(50 / (s - 20)) + (210 / s) = 4
To simplify the equation, we can multiply all terms by s(s - 20) to eliminate the denominators:
50s + 210(s - 20) = 4s(s - 20)
Now, we can solve for 's':
50s + 210s - 4200 = 4s^2 - 80s
Combine like terms:
254s - 4200 = 4s^2 - 80s
Rearrange the equation to form a quadratic equation:
4s^2 - 334s + 4200 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula.
After solving the quadratic equation, we find two possible values for 's'. Let's assume one of them is the average speed of the train.
Once we have the value of 's', we can find the average speed of the car by subtracting 20 mph from 's'.
So, the average speed of the car is 's - 20' mph, and the average speed of the train is 's' mph.
It's important to note that this formula is identical to that of constant speed.
Average speed is measured in units of distance per time. Common units include miles per hour (mph), kilometers per hour (kph), meters per second (m/s), or feet per second (ft/s).
Average speed = distance travelled / elapsed time