What was the speed of the gypsy?

Question

The gypsies were 225 miles apart at 2:00p.m. and were headed toward each other. If they met at 4:30p.m. and one was trveling 20 miles per hour faster than the other, what was the speed of each gypsy?

Answer 1

Here is an easy way to figure this out.

They cover the distance between them (225 miles) in 2.5 hours, so their combined speed is 225 / 2.5 = 90 miles per hour.
Let s be the speed of the slower one. Then the speed of the faster one is s + 20, and s + (s + 20) = 90, or 2s = 70. Then s = 35 mph and s + 20 = 55 mph.

Answer 2

lets say the speeds are respectively x and y .

from the first statment , we know the gipsies met after covering 225 miles , so the sum of the distances made by each gypsy equals 225
distance covered by first equals time multiplied by speed (x)
distance covered by second is time multiplied by speed(y)

the time they took to travel this distance can be calculated from the times of depart and arrival
4:30 - 2:00 = 2.5 hours


2.5 hrs *x +2.5*y=225

from the last part of the question
one is more than the other by 20
lets say x= y+20

if we replace the x in the first equation with its y value (y+20) we get

2.5 (y+20) + 2.5 y = 225
5y +50 = 225
5y = 175
y=35 miles an hour

from the second equation
x=y+20= 55 miles an hour .

so your answer is 55 miles/hour and 35 miles/hour