Question 469808
Distance = rate * time


Motorcycle: Distance = 50mph * x hours
Car: Distance = 40mph * (x+3) hours (since the car had 3 extra hours to drive)


When they meet with each other, they will have gone the same distance, so you can set these equal to each other: {{{50*x=40*(x+3)}}}


Notice that we need to solve for x, but that will give us the number of hours; you'll have to plug back in for distance.


You said you just need the formula, so stop reading now if you don't want more help solving it :)


First, distribute 40 through the parentheses: {{{50x=40x+120}}}
Subtract 40x from both sides to bring all of the variables to the left: {{{10x=120}}}
Divide through by 10 to isolate x: {{{x=12}}}
12 hours after the motorcycle leaves, it will meet up with the car.


Distance: 50 mph * 12 hours = 600 miles from where they started


You can check with the car's formula: 40 mph * (12+3) hours = 600 miles.