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Carter traveled $95$ miles from Sartell to Target Field by car for part of the way and then took the Lioit Rail Train for the remainder of the trip. The car was traveling an average rate of $60$ mph and we Lioit Rall Train averaged $\newline$ $90$ mph. If the total trip took $1.5$ hours. How long did Carter travel by train?

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Evaluate variable expressions: word problems

Full solution

Q. Carter traveled

95

miles from Sartell to Target Field by car for part of the way and then took the Lioit Rail Train for the remainder of the trip. The car was traveling an average rate of

60

mph and we Lioit Rall Train averaged

\newline

90

mph. If the total trip took

1.5

hours. How long did Carter travel by train?

Define travel time equation: Let's define the time Carter traveled by car as $t_c$ hours and by train as $t_t$ hours. The total travel time is given as $1$ . $5$ hours. So, we write the equation: $\newline$ $t_c + t_t = 1.5$
Use rate-time-distance relationship: We know the car traveled at $60$ mph and the train at $90$ mph. Let's assume the distance traveled by car is $d_c$ miles and by train is $d_t$ miles. Using the rate-time-distance relationship: $\newline$ $d_c = 60t_c$ $\newline$ $d_t = 90t_t$
Write total distance equation: Since the total distance is $95$ miles, we can write another equation: $\newline$ $d_c + d_t = 95$ $\newline$ Substituting the expressions for $d_c$ and $d_t$ from the previous step: $\newline$ $60t_c + 90t_t = 95$

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