The more accurate value is 27.272727... where the "27"s go on forever.
The answer in fraction form is 300/11. I prefer the approximate form better since it's easier to conceptualize "27 minutes" as opposed to "300/11 minutes".
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Explanation:
x = time it takes the car to pass the truck (in minutes).
The car enters the highway and drives for x minutes until it passes the truck.
The truck is on the highway for 5 extra minutes, since it got a head start, so the truck travels for x+5 minutes until the car passes it.
Everything so far is talking about minutes and not hours. However, the speed values are in miles per hour. So let's convert everything to "miles per minute". To do so, we divide by 60.
I'll leave the fraction as it is. Optionally you can convert to decimal form. Those speeds represent the truck and the car in that order.
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The car has these properties
Using the distance = rate*time formula, we then can see that the car travels (71/60)x miles
The truck has these properties
So the truck travels a distance of x+5 miles
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The two vehicles must travel the same distance if we want the car to overtake the truck. In other words, the car and truck must be tied for the car to eventually pass the truck.
Truck's Distance = Car's Distance
x+5 = (71/60)x
60(x+5) = 71x
60x+300 = 71x
300 = 71x-60x
300 = 11x
11x = 300
x = 300/11
x = 27.272727 which is approximate. The "27"s go on forever.
Rounding to the nearest whole minute, we get approximately 27 minutes which is the time it takes for the car to pass the truck. This is where we defined the starting point being after the car enters the highway.
