Distance Traveled by Car - word problem:
It takes a man 4 hours to reach a destination 1325 miles from his home. He drives to the airport at an average speed of 50 miles per hour, and the average speed of his plane trip is 500 miles per hour. How far does he travel by each mode of transportation?
Solution:
Step 1. Let x = Distance Traveled by Car (in miles)
Step 2. Then,
1325 - x = Distance Traveled by Plane (in miles)
and, using Equation 2-14,
x/50 = Time Traveled by car (in hours)
1325 - x/ 500 = Time Traveled by Plane (in hours)
Step 3. Total Time = (Time Traveled by Car) + (Time Traveled by Plane)
4 hours = x/50 hours + 1325 - x/500 hours
Step 4. Solving for x:
4 = x/50 + 1325 - x / 500
4 = 10x + 1325 -x/ 500
(500)4 = 9x + 1325 /500 (500)
2000 = 9x + 1325
2000 - 1325 = 9x
685 = 9x
9x /9 = 675/9
x = 75 miles
Solving for the other unknowns:
x/50 = Time Traveled by Car (in hours)
x/50 = 75 /50
x/50 = 1 ½ hours
1325 - x/500 = Time Traveled by plane (in hours)
1325 - x/500 = 1324 - 75 /500
1325 - x /500 = 1250/500 = 2 ½ hours
1325 - x = Distance Traveled by Plane (in miles)
1325 - x = 1325 -75
1325 - x = 1250 miles
Answers:
Distance Traveled by Car = 75 miles
Distance Traveled by Plane = 1250 miles
Step 5. The total distance traveled is 1325 miles.
75 miles + 1250 miles = 1325 miles
The average speed via car is 50 miles per hour.
75 miles/1 ½ hours = 50miles per hour
The average speed via plane is 500 miles per hour.
1250 miles/2 ½ hours = 500 miles per hour
The total time traveling is 4 hours.
1½ hours + 2½ hours = 4 hours
Therefore, the answers check.