You are eating lunch at your favorite cafe and your friend calls and says he wan

Question

You are eating lunch at your favorite cafe and your friend calls and says he wants to meet you. He is calling from a city 145 miles away and wants to meet you somewhere between the two locations. He says he will start driving right away, but you need 29.0 minutes to finish your lunch before you can begin driving. If your friend plans to drive at 75.0 mph and you plan to drive at 55.0 mph, how long will your friend be driving before he meets you? (Ignore acceleration and assume the highway forms a straight line.)

Explanation / Answer

let x mile be the distance traveeld by your friend
then the distance traveeled by you is 145-x mile

let t mins be the time taken by you to reach your friend
then time tken by your frirnd to reach you is (29+t)minutes = (29+t)/60 hours

then total distance travelled by you and your friend is 145 miles

[75*(29+t)/60] + (55*t/60) = 145

t= 50.2 minutes

then distance travelled by your friend is x = 75*(29+50.2)/60 = 99 miles and drived for 29+50.2 = 79.2 minutes

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