Answer:
The system of linear equations that can be used to determine the time that each of the trains has been traveling is:
E + W = 4 ....... Equation 1
95 E + 110W = 400 ......Equation 2
Hence,
An Eastbound train has been travelling for = (E) = 2.67 hours
A Westbound train has been travelling for = (W) = 1.33 hours
Explanation:
An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different times. After 4 hours, they are 4 00 miles apart. Which system of linear equations can be used to determine the time that each of the trains has been traveling?
Speed = Distance/Time
Distance = Speed × Time
Let the time
An Eastbound train = (E)
A Westbound train = (W)
E + W = 4 hours ....... Equation 1
95mph × E + 110mph × W = 400 miles
95 E + 110W = 400 miles ......Equation 2
The system of linear equations that can be used to determine the time that each of the trains has been traveling is:
E + W = 4 ....... Equation 1
95 E + 110W = 400 ......Equation 2
E = 4 - W
We substitute 4 - W for E in Equation 2
95 (4 - W) + 110W = 400
380 - 95W + 110W = 400
Collect like terms
95W - 110W = 400 - 380
15W = 20
W = 20/15
W = 1.3333333333 hours
≈ 1.33 hours
E = 4 - W
E = 4 - 1.33 hours
E = 2.67 hours
Therefore,
An Eastbound train has been travelling for = (E) = 2.67 hours
A Westbound train has been travelling for = (W) = 1.33 hours