SOLUTION: A motorist travels travels 400 km partly at 100 km/hr and partly at 80 km/h. If he had traveled at 80 kn/hr instead of 100 km/hr and had 100 km/h instead of 80 km/hr, the journey w

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A motorist travels travels 400 km partly at 100 km/hr and partly at 80 km/h. If he had traveled at 80 kn/hr instead of 100 km/hr and had 100 km/h instead of 80 km/hr, the journey w      Log On


   

Question 1129074: A motorist travels travels 400 km partly at 100 km/hr and partly at 80 km/h. If he had traveled at 80 kn/hr instead of 100 km/hr and had 100 km/h instead of 80 km/hr, the journey would have taken 0.5 h longer. find his time for the trip.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let the distances (km) for the two parts of the trip be x and 400-x. Then

The total number of hours for the trip, at 100km/hr for the first part and 80km/hr for the second, was

x%2F100%2B%28400-x%29%2F80

If the two speeds had been switched, the total number of hours would have been

x%2F80%2B%28400-x%29%2F100

The second trip would have taken 0.5 hours longer:

x%2F80%2B%28400-x%29%2F100+=+x%2F100%2B%28400-x%29%2F80%2B0.5

Multiply through by the LCM, 400:

5x%2B4%28400-x%29+=+4x%2B5%28400-x%29%2B200

Solve....

5x%2B1600-4x+=+4x%2B2000-5x%2B200
2x+=+600
x+=+300

He traveled at 100km/hr for 300 km (3 hours) and at 80 km/hr for 100 km (1.25 hours); total time 4.25 hours.

If the speeds had been switched, he would have traveled at 80km/hr for 300 km (3.75 hours) and 100km at 100km/hr (1 hour); total time 4.75 hours.