Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours. The equation 3t = 5(3 – t) can be used to find the time it took Stu to hike one way. How long did it take Stu to hike the trail one way? hours How long is the trail? miles What is the total distance Stu travelled? miles
1 answer:
Answer:
Time taken to travel at 3 miles = 1.875
Time taken to travel at 5miles = 1.125
Total distance = 11.25
Step-by-step explanation:
D = speed x time
Time = distance/speed
Time at 3 miles per hour and 5 miles per hour
T1 = d/3
T2 = d/5
Total time = 3 hours
T1+t2 = 3 hours
d/3 + d/5 = 3
= d(1/2+1/5) = 3
d(5+3/15) = 3
d(8/15) = 3
We cross multiply
8d = 45
d = 45/8
= 5.625 miles
Total distance = 2d
2x5.625 = 11.25 miles
Since d is now known
T1 = 5.625/3 = 1.875 hours also 1 hour 52.5 minutes
T2 = 5.625/5 = 1.125 hours = 1 hour 7.5 minutes
Total distance 2xd = 11.25
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