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 145miles away and wants to meet you somewhere between the two locations. he says he will start driving right away, but you need 30.0 minutes to finish your lunch before you can begin driving. If your friends plans to drive at 70 mph and you plan on driving at 40mph, how long will your friend be driving before he meets you?

Answer 1

Speed =Distance /Time

Let $d_{f}$ be the distance driven by friend

and $d_{i}$ be the distance driven by me

$d_{i}+d_{f}=145miles$

Let $t_{f}$ be the time taken by friend for drive

so my driving time is $(t_{f}-0.5hr)$

Distance =Speed*time

$d_{i}+d_{f}=145miles$

$40mph*(t_{f}-0.5hr)+70mph*t_{f}=145miles$

$40*(t_{f}-0.5)+70*t_{f}=145$

$40t_{f}-20+70t_{f}=145$

$110t_{f}=145+20$

$t_{f}=165/110$

ANSWER: ${\color{Red} t_{f}=1.5hr}$

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