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 125 miles away and wants to meet you somewhere between the two locations. He says he will start driving right away, but you need 25.0 minutes to finish your lunch before you can begin driving. If your friend plans to drive at 65.0 mph and you plan to drive at 60.0 mph, how long will your friend be driving before he meets you? (Ignore acceleration and assume the highway forms a straight line.)

How far will you have traveled by the time you meet him?

Explanation / Answer

we need 27 minutes for lunch

distance travelled by friend in 27 minutes = 70*27/60 = 31.5 miles

actual distance = 135 miles

now after 27 minutes (our start time) distance = 135-31.5 = 103.5 miles

now relative velocity between friends = 70- (-60) = 130

because opposite directions

so meeting time = 103.5/ 130 = 47.77 minutes

now distance travelled by friend before he meets me

= 31.5 + 70*47.77/60 = 87.23 miles

distance travelled by me = 135-87.23 = 47.77 miles

verification- distance = 60*0.7962 = 47.77 miles

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