Asked by 123
Suppose you wish to average 40 mph on a trip and find that when you are half the distance to your destination you have averaged 30 mph. How fast should you travel in the remaining half of the trip to attain an overall average of 40 mph?
I think the answer is35mph. (40+30)/2 =35. Am I right?
I think the answer is35mph. (40+30)/2 =35. Am I right?
Answers
Answered by
oobleck
Did you check your answer? Say the trip is 120 miles (the actual distance does not matter)
60mi at 30mi/hr = 2 hours
So, you need to cover the remaining 60 miles in 1 hour to have an average speed of 120mi/3hr = 40 mi/hr
In fact, you should have seen immediately that your answer was wrong. How could driving partway at 30 and the rest at 35 produce an average speed of 40? Always do a sanity check on your answer to see whether it even makes sense.
time = distance/speed. So, for a trip of x miles,
(x/2)/30 + (x/2)/s = x/40
In other words,
1/60 + 1/(2s) = 1/40
s = 60
60mi at 30mi/hr = 2 hours
So, you need to cover the remaining 60 miles in 1 hour to have an average speed of 120mi/3hr = 40 mi/hr
In fact, you should have seen immediately that your answer was wrong. How could driving partway at 30 and the rest at 35 produce an average speed of 40? Always do a sanity check on your answer to see whether it even makes sense.
time = distance/speed. So, for a trip of x miles,
(x/2)/30 + (x/2)/s = x/40
In other words,
1/60 + 1/(2s) = 1/40
s = 60
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