The distance from Town X to Town Y is 1,650 miles
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Average speed of the man on the 1st leg of the trip = 60 mph
Average speed of the man on the 2nd leg of the trip = 50 mph
Time of the trip = 1/2 hour longer than the time he would take if he made the round trip at an average of 55 mph
2. Let's resolve the question what is the distance from Town X to Town Y.
Distance from Town X to Town Y = x
Time the man drove on the 1st leg of the trip = x/60
Time the man drove on the 2nd leg of the trip = x/50
Time the man would take if he made the round trip at an average speed of 55 mph = 2x/55
For calculating x we use the following formula:
x/60 + x/50 - 1/2 = 2x / 55
(50x + 60x - 1,500)/3,000 = 2x/55 (Finding common denominators on both sides of the equation)
50x + 60 x - 1,500 = 3,000 (2x/55) (Multiplying by 3,000 at both sides of the equation)
50x + 60x - 1,500 = 600 * 2x/11 (Dividing by 5 at the right numerator and denominator)
550x + 660x - 16,500 = 1,200x (Multiplying by 11 at both sides of the equation)
1,210x - 16,500 = 1,200x
1,210x - 1,200x = 16,500 (Subtracting 1,200x at both sides and adding 16,500 at both sides)
10x = 16,500
x = 16,500/10 (Dividing by 10)
x = 1,650 miles
3. Let's prove that x = 1,650 is correct
x/60 + x/50 - 1/2 = 2x / 55
1,650/60 + 1,650/50 - 1/2 = 2 * 1,650/55
27.5 + 33 - 0.5 = 2 * 30 (We replaced 1/2 = 0.5)
60.5 - 0.5 = 60
60 = 60
We proved that x = 1,650 is correct
4. Time of the trip
1st leg at 60 miles per hour takes 27.5 hours
2nd leg at 50 miles per hour takes 33 hours
Round trip at 55 miles per hours takes 60 hours
27.5 + 33 = 60.5
It's proved that it takes 0.5 hours more driving the 1st leg at an average speed of 60 miles per hour and the 2nd leg at an average speed of 50 miles per hour than the round trip an average speed of 55 miles per hour