SOLUTION: A fire truck is called into a scene. Three minutes later, a second truck is called. The first truck averages on 30 miles per hour, but the second truck averages 60 miles per hour.

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Question 343669: A fire truck is called into a scene. Three minutes later, a second truck is called. The first truck averages on 30 miles per hour, but the second truck averages 60 miles per hour. The trucks travel a total of 12 miles and arrive at the same time.
How long from the first call did the trucks take to arrive? How far did each travel?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let represent the distance in miles traveled by the first truck.

Let represent the travel time of the first truck in minutes.

Since we are expressing time in minutes, convert 30 miles per hour to 1/2 mile per minute and 60 miles per hour to 1 mile per minute.

The first truck:



If the first truck traveled miles, then the second truck traveled miles. If the first truck traveled for minutes, then the second truck, having been called 3 minutes later, traveled minutes.

The second truck:



(Remember, the second truck's rate was 1 mile per minute)

Solve for



Now we have two expressions each of which is equal to , so set them equal to each other:



Solve for to get the time for the first truck. Substitute into to find the distance for the second truck.

Subtract to get the time for the second truck.

Subtract to get the distance for the second truck.

John

My calculator said it, I believe it, that settles it
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