Traffic is heavy on the Dallas to Ft Worth leg of your trip

Traffic is heavy on the Dallas to Ft. Worth leg of your trip and you are only able to average 30 miles per hour

How fast must you travel on the return leg in order to average 60 miles an hour for the entire trip?

Solution

round trip distance is 60 miles.

rate * time = distance

to travel 60 miles at 60 miles per hour, you have to take 1 hour for the round trip.

this would make the formula:

60 * 1 = 60 which would be true.

the total time it should take would be 1 hour.

you traveled the first leg at 30 miles per hour.

this means that the formula of rate * time = distance for the first leg becomes:

30 * x = 30.

this means that it took 1 hour to travel 30 miles.

this means that you will never be able to average 60 miles per hour for the round trip.

example:

you traveled 30 miles per hour for the first part of the trip.

that took you 1 hour.

you travel 3000 miles per hour for the return trip.

since rate * time = distance, then the formula becomes:

3000 * x = 30

x = 30/3000 = 3/300 = .01 hours

total time it takes is 1.01 hours.

that\'s 1 hour for the going leg and .01 hours for the return leg.

average rate for the round trip is based on the formula of rate * time = distance:

x * 1.01 = 60

rate you traveled is 60/1.01 = 59.40594059 miles per hour.

you can approach 60 miles per hour overall but you will never quite make it because your divisor will always be a very small amount greater than 1.

this means that your numerator will always be a very small amount less than 60.