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Elena cycled a charity route at a constant speed. How many hours did it take Elena to complete the route?
(1) If Elena had cycled 6 kilometers per hour faster than she actually did, she would have completed the route in 3 hours 45 minutes.
(2) If Elena had cycled 25 percent faster than she actually did, she would have completed the route in 4 hours.
(1) If Elena had cycled 6 kilometers per hour faster than she actually did, she would have completed the route in 3 hours 45 minutes.
(2) If Elena had cycled 25 percent faster than she actually did, she would have completed the route in 4 hours.
30 May 2026, 09:28
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Official Solution:
Elena cycled a charity route at a constant speed. How many hours did it take Elena to complete the route?
(1) If Elena had cycled 6 kilometers per hour faster than she actually did, she would have completed the route in 3 hours 45 minutes.
Let Elena’s actual speed be \(v\) kilometers per hour and the route length be \(D\) kilometers. This statement gives \(D = (v + 6) * 3.75\). The actual time is \(\frac{D}{v} = \frac{3.75 * (v + 6)}{v}\), which depends on \(v\). Not sufficient.
(2) If Elena had cycled 25 percent faster than she actually did, she would have completed the route in 4 hours.
If her speed were 25 percent greater, it would be \(1.25v\). This statement gives \(D = 1.25v * 4 = 5v\), so the actual time is \(\frac{D}{v} = 5\) hours. Sufficient.
Answer: B
Elena cycled a charity route at a constant speed. How many hours did it take Elena to complete the route?
(1) If Elena had cycled 6 kilometers per hour faster than she actually did, she would have completed the route in 3 hours 45 minutes.
Let Elena’s actual speed be \(v\) kilometers per hour and the route length be \(D\) kilometers. This statement gives \(D = (v + 6) * 3.75\). The actual time is \(\frac{D}{v} = \frac{3.75 * (v + 6)}{v}\), which depends on \(v\). Not sufficient.
(2) If Elena had cycled 25 percent faster than she actually did, she would have completed the route in 4 hours.
If her speed were 25 percent greater, it would be \(1.25v\). This statement gives \(D = 1.25v * 4 = 5v\), so the actual time is \(\frac{D}{v} = 5\) hours. Sufficient.
Answer: B
