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13 Jan 2022, 05:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:10) correct
27%
(01:36)
wrong
based on 55
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A plane travels certain distance d in time t hours. If the ratio of the speed of the plane if it had taken half an hour less to cover d to the speed of the plane if it had taken half an hour more to cover d is 5:3, what is the value of t (in hours)?
A. 1
B. 2
C. 3
D. 4
E. 6
A. 1
B. 2
C. 3
D. 4
E. 6
14 Jan 2022, 02:16
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Formula for speed: \(\frac{Distance}{Time}\)
Speed during Normal Trip: \(\frac{d}{t}\)
Speed if it had taken half an hour less: \(\frac{d}{t-0.5}\)
Speed if it had taken half an hour longer: \(\frac{d}{t+0.5}\)
Ratio of speeds had the trip taken shorter or longer:
\(\frac{5}{3} = \frac{\frac{d}{t-0.5}}{\frac{d}{t+0.5}}\)
\(\frac{5d}{t+0.5} = \frac{3d}{t-0.5}\)
\(5d(t-0.5) = 3d(t+0.5)\)
Divide through by d
\(5(t-0.5) = 3(t+0.5)\)
\(5t - 2.5 = 3t + 1.5\)
\(2t = 4\)
\(t = 2\)
Answer B
Speed during Normal Trip: \(\frac{d}{t}\)
Speed if it had taken half an hour less: \(\frac{d}{t-0.5}\)
Speed if it had taken half an hour longer: \(\frac{d}{t+0.5}\)
Ratio of speeds had the trip taken shorter or longer:
\(\frac{5}{3} = \frac{\frac{d}{t-0.5}}{\frac{d}{t+0.5}}\)
\(\frac{5d}{t+0.5} = \frac{3d}{t-0.5}\)
\(5d(t-0.5) = 3d(t+0.5)\)
Divide through by d
\(5(t-0.5) = 3(t+0.5)\)
\(5t - 2.5 = 3t + 1.5\)
\(2t = 4\)
\(t = 2\)
Answer B
14 Jan 2022, 22:18
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We can solve by using simple ratio concept (componendo/dividendo)
s1 = d/(t-1/2)
s2 = d/(t+1/2)
s1/s2 = 5/3
(d/(t-1/2))/(d/(t+1/2)) = 5/3 -> (t+1/2)/(t-1/2) = 5/3 = (2+1/2)/(2-1/2) -> t = 2 (option B)
s1 = d/(t-1/2)
s2 = d/(t+1/2)
s1/s2 = 5/3
(d/(t-1/2))/(d/(t+1/2)) = 5/3 -> (t+1/2)/(t-1/2) = 5/3 = (2+1/2)/(2-1/2) -> t = 2 (option B)
14 Jan 2022, 23:03
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Given: A plane travels certain distance d in time t hours.
Asked: If the ratio of the speed of the plane if it had taken half an hour less to cover d to the speed of the plane if it had taken half an hour more to cover d is 5:3, what is the value of t (in hours)?
Speed of the plan s = d/t
The ratio of the speed of the plane if it had taken half an hour less to cover d to the speed of the plane if it had taken half an hour more to cover d is 5:3.
{d/(t-.5)}/{d/(t+.5)} = 5/3
(t+.5)/(t-.5) = 5/3
t = 2 hours
IMO B
Asked: If the ratio of the speed of the plane if it had taken half an hour less to cover d to the speed of the plane if it had taken half an hour more to cover d is 5:3, what is the value of t (in hours)?
Speed of the plan s = d/t
The ratio of the speed of the plane if it had taken half an hour less to cover d to the speed of the plane if it had taken half an hour more to cover d is 5:3.
{d/(t-.5)}/{d/(t+.5)} = 5/3
(t+.5)/(t-.5) = 5/3
t = 2 hours
IMO B
