Wendy took a trip from city A to city B, a distance of 560 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 40 mi/h, and the train averaged 110 mi/h. The entire trip took
10
1
2
h. How long did Wendy spend on the train?
To find out how long Wendy spent on the train, we need to calculate the time she spent on the bus first. We can use the formula Time = Distance / Speed.
The distance traveled on the bus can be found by subtracting the distance traveled on the train from the total distance. So, the distance traveled on the bus is 560 mi - x mi, where x represents the distance traveled on the train.
Using the formula for time, the time spent on the bus can be calculated as (560 - x) / 40.
Since the entire trip took 10 and 1/2 hours, the total time can be expressed as the sum of the time spent on the bus and the time spent on the train: (560 - x) / 40 + x / 110 = 10.5.
To solve this equation for x, we multiply both sides by the common denominator of 40 and 110, which is 4400. This gives us: 110(560 - x) + 40x = 10.5 * 4400.
Now, let's simplify the equation: 61600 - 110x + 40x = 46200.
Combining like terms, we get: 61600 - 70x = 46200.
To isolate x, we subtract 61600 from both sides: -70x = -15400.
Dividing both sides by -70, we find that x = 220.
Now that we know the distance traveled on the train is 220 mi, we can calculate the time spent on the train: Time = Distance / Speed = 220 mi / 110 mi/h = 2 hours.
Therefore, Wendy spent 2 hours on the train.