The distance d a train travels varies directly with the amount of time t that has elapsed since departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after 4 hours?
(1 point)
Responses
100
100
200
200
232.5
232.5
300The distance d a train travels varies directly with the amount of time t that has elapsed since departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after 4 hours?
(1 point)
Responses
100
100
200
200
232.5
232.5
300The distance d a train travels varies directly with the amount of time t that has elapsed since departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after 4 hours?
(1 point)
Responses
100
100
200
200
232.5
232.5
300
To find the distance the train traveled after 4 hours, we can use the concept of direct variation.
If the distance varies directly with time, then we can write the equation as d = kt, where k is the constant of variation.
We are given that the train traveled 475 miles in 9.5 hours. We can use this information to find the value of k.
475 = k * 9.5
Dividing both sides by 9.5, we get:
k = 475/9.5 = 50
Now that we have the value of k, we can find the distance the train traveled after 4 hours.
d = kt = 50 * 4 = 200 miles
Therefore, the train traveled 200 miles after 4 hours.
To solve this problem, we can assume that the distance traveled by the train is directly proportional to the time elapsed. This can be expressed as:
d = kt
where d is the distance traveled, t is the time elapsed, and k is a constant.
Given that the train travels 475 miles in 9.5 hours, we can use this information to find the value of k:
475 = k * 9.5
Dividing both sides of the equation by 9.5, we get:
k = 475 / 9.5 = 50
Now we can use the value of k to find the distance traveled after 4 hours:
d = 50 * 4 = 200
Therefore, the train traveled 200 miles after 4 hours.