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20 Jul 2023, 11:16
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D
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Difficulty:
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70% (02:27) correct
30%
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wrong
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Ahab ran southeast at 10 km per hour. An hour later, Eli ran southeast, along the same route as Ahab, at 15 kilometers per hour. If Eli arrived at his destination 30 minutes before Ahab arrived at the same destination, how long, in hours, was Ahab's journey?
A) 3.0
B) 3.5
C) 4.0
D) 4.5
E) 5.0
A) 3.0
B) 3.5
C) 4.0
D) 4.5
E) 5.0
29 Sep 2023, 23:08
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Dear Experts KarishmaB Bunuel GMATNinja
Please check if my method is correct
As we know Distance = Speed x Distance
Let x be the time taken by Ahab and D is the total distance
Equation for Ahab :
10*x = D
Equation for Eli :
15*(x-1.5) = D
here 1.5 = 1 (Eli started 1 hour late) + 0.5 (Eli reached 0.5 hours early)
So 10*x = 15(x-1.5), which gives x = 4.5 hours
Please check if my method is correct
As we know Distance = Speed x Distance
Let x be the time taken by Ahab and D is the total distance
Equation for Ahab :
10*x = D
Equation for Eli :
15*(x-1.5) = D
here 1.5 = 1 (Eli started 1 hour late) + 0.5 (Eli reached 0.5 hours early)
So 10*x = 15(x-1.5), which gives x = 4.5 hours
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21 Jul 2023, 23:40
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GianKR
You can do this using the concept of races or relative speed.
Method 1: Relative Speed
When Ahab ran for an hour, he covered 10 km. Eli completed the distance ahead of Ahab by half an hour (Ahab would have needed half an hour to complete the distance which means the distance was 5 km since his speed is 10 kmph)
So Eli ran a distance of 10 + 5 = 15 km extra at an extra speed of 15 - 10 = 5 kmph. So Eli took 15/5 = 3 hrs to complete this distance.
Then Ahab took 1+ 3 + 0.5 = 4.5 hrs to complete this distance.
Method 2:Races
Make a races diagram:
E ----(10 km)------ A--------------------(d km)-------------------A ------(5 km)----E
In the same time, Eli covered 10 + d + 5 km while Ahab covered only d km.
Since their speeds are in the ratio 3:2, the distance covered will be in the ratio 3:2 i.e. d+15 : d
Hence, the difference of 1 is actually 15 so d must be 30 km.
Then total distance is 10 + 30 + 5 = 45 km for which Ahab took 45/10 = 4.5 hrs
Answer (D)
