Question

Some friends are leaving a party in Princeton to go home. One group takes a taxi uptown, traveling north at 34 miles per hour. The rest of the friends share another taxi, traveling south at 42 miles per hour. If the two taxis depart at the same time, how much time will pass before they are 10 miles apart?

Answer 1

• Time=Distance/Speed

Equations are

• 10/34=t=>10=34t=>t=10/34=5/17--(1)
• 10-x/42=t=>42t=10-x-(2)

Put t in eq(2)

$\\ \tt\hookrightarrow 42(5/17)=10-x$

$\\ \tt\hookrightarrow 210/17=10-x$

$\\ \tt\hookrightarrow 12.3=10-x$

$\\ \tt\hookrightarrow x=|-2.3|=2.3m$

Now

$\\ \tt\hookrightarrow 42t=10-2.3$

$\\ \tt\hookrightarrow 42t=7.7$

$\\ \tt\hookrightarrow t\approx 0.6h$