John can drive 240 miles in the same time as it takes George to drive 220 miles. If John drives 5 mph faster than George, then how fast does John drive?
Use J for John's speed and G for George's:
J = G + 5 (John drives 5mph faster)
240 = J * t (distance is rate times time)
220 = G * t
Divide both sides of the second equation by J and both sides of the third by G:
t = 240 / J
t = 220 / G
Since the time is the same, set the two right sides equal to each other:
240 / J = 220 / G
Substitute G + 5 (from the first equation) for J:
240 / (G + 5) = 220 / G
Cross-multiply:
240G = 220(G + 5)
Multiply out the right side:
240G = 220G + 1100
Subtract 220G from both sides:
20G = 1100
Divide both sides by 20:
G = 1100 / 20 = 55
George drives at 55 mph. Going 5 mph faster, John drives at 60 mph.
Ok, John's speed is 240/t and George's is 220/t and we are given 240/t - 220/t = 5
First multiply everything by t to get rid of the fractions.
240 - 220 = 5t
5t = 20
t = 4
George's speed is 55 and John's is 60. Time is 4 hours.
240/J = 220/(J-5)
24J-120 = 22J
2J = 120
J = 60 mph
Comments
Use J for John's speed and G for George's:
J = G + 5 (John drives 5mph faster)
240 = J * t (distance is rate times time)
220 = G * t
Divide both sides of the second equation by J and both sides of the third by G:
t = 240 / J
t = 220 / G
Since the time is the same, set the two right sides equal to each other:
240 / J = 220 / G
Substitute G + 5 (from the first equation) for J:
240 / (G + 5) = 220 / G
Cross-multiply:
240G = 220(G + 5)
Multiply out the right side:
240G = 220G + 1100
Subtract 220G from both sides:
20G = 1100
Divide both sides by 20:
G = 1100 / 20 = 55
George drives at 55 mph. Going 5 mph faster, John drives at 60 mph.
Ok, John's speed is 240/t and George's is 220/t and we are given 240/t - 220/t = 5
First multiply everything by t to get rid of the fractions.
240 - 220 = 5t
5t = 20
t = 4
George's speed is 55 and John's is 60. Time is 4 hours.
240/J = 220/(J-5)
24J-120 = 22J
2J = 120
J = 60 mph