Solve the following word problem. A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph. What is the distance from Town X to Town Y? a0 miles

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