If I am going 75 miles per hour and my friend is going 55 mi

If I am going 75 miles per hour and my friend is going 55 miles per hour and he leaves 10 minutes before me, how long will it take me to catch him?

Solution

d=rt or
d=75(x-1/6)
d=55x
The 2 distances are equal thus:
75(x-1/6)=55x
75x-75/6=55x
75x-55x=75/6
20x=75/6
20x=12.5
x=12.5/20
x=5/8 or .625 or 37.5 minutes after your friend leave you will catch up with him.
Proof:
75(5/8-1/6)=55*5/8
75(5*6-8)/48=275/8
75(30-8)/48=275/8
75*22/48=275/8
1,650/48=275/8
48*275=8*1,650
13,200=13,200