A traveler walks a certain distance. Had he gone half a kilometer an hour…
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A traveler walks a certain distance. Had he gone half a kilometer an hour faster, he would have walked it in 4/5 of the time, and had he gone half a kilometer an hour slower, he would have walked 2½ hour longer. What is the distance?
- A.
15 km
- B.
10 km
- C.
7.5 km
- D.
12 km
Attempted by 517 students.
Show answer & explanation
Correct answer: A
Let s be the original speed in km/h and t the original time in hours. Then distance d = s * t.
Faster case: If the traveler went 0.5 km/h faster, he would take 4/5 of the time. So (s + 0.5) * (4/5)t = s * t.
From this equation (divide both sides by t): (4/5)(s + 0.5) = s. Solving gives (4/5)s + 0.4 = s, so (1/5)s = 0.4 and s = 2 km/h.
Slower case: If the traveler went 0.5 km/h slower, he would take 2.5 hours longer. So (s - 0.5) * (t + 2.5) = s * t.
Substitute s = 2 into this equation: (2 - 0.5)*(t + 2.5) = 2t -> 1.5t + 3.75 = 2t -> 0.5t = 3.75 -> t = 7.5 h.
Distance: d = s * t = 2 * 7.5 = 15 km.
Answer: 15 km