Distance traveled by car - word problem, Mathematics

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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.


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