A cargo plane left Rome and flew south at an average speed of 168mph. A passenger plane left 1.5 hours later and flew in the same direction but with an average speed of 268.8mp. How long did the cargo plane fly before the passenger plane caught up?

*Would the answer be either 4 hours or 2.5 hours?

Question

A cargo plane left Rome and flew south at an average speed of 168mph. A passenger plane left 1.5 hours later and flew in the same direction but with an average speed of 268.8mp. How long did the cargo plane fly before the passenger plane caught up?

*Would the answer be either 4 hours or 2.5 hours?

calculusxy · Answer

@Nnesha @SolomonZelman @Hero

mathmale · Answer

It's possible that sketching this situation would help, 'tho one can solve the problem without a sketch.

Let t represent the # of hours flown by the cargo plane.
How would you represent the # of hours flown by the passenger plane?

mathmale · Answer

How would you represent the total distance flown by the cargo plane?
Same question, for the passenger plane ... ?

calculusxy · Answer

|dw:1452208452538:dw|

calculusxy · Answer

I solve for T to get 4 hours. But I am not sure whether I should subtract the 1.5 from T (passenger) or leave it as it is .

mathmale · Answer

Remember, t is the flight time of the cargo plane, which flies more slower than does the passenger plane.  Given that, how would you represent the time, t, at which the passenger plane catches up with the cargo plane?

calculusxy · Answer

do you mean to do 4 - 2.5 ?

mathmale · Answer

Before you'd try answering that, I'd suggest you try checking t=4 hours.  Does the pass. plane catch up with the cargo plane in 4 hours?   Please show your work.

mathmale · Answer

Please double check that you have the airspeeds correct.  168 and 168.8 mph are very close together, meaning that if these are truly the correct numbers, it'd take a LONG time for the passenger plane to catch up with the cargo plane.   In fact, I got t=316.5 hours, which I regard as ridiculous.  Both planes would have run out of fuel long before that.

calculusxy · Answer

Sorry there was a typo. It was supposed to be 268.8mph. I apologize for the inconvenience

mathmale · Answer

Apologies.  I'm the one who should have double checked.  Your original problem statement does say 268.8 hours.

Have you been using 168 and 268.8 hours in your calculations?

calculusxy · Answer

yes

mathmale · Answer

I've obtained one result, one of which is very nearly the same as one of your two results.
I don't see how you could have come up with two results. 

Mind checking?

calculusxy · Answer

168t = 268.8(t - 1.5)
168t = 268.8t - 403.20
-100.8t = -403.20
t = 4

calculusxy · Answer

@mathmale

mathmale · Answer

Great.  Have you checked your answer?  How would you know whether it's really t=4 hours?