Cynthia’s afternoon train normally arrives at her station at 5:30 pm each day, where she is picked up by Alan and driven home. One day she was on an earlier train which arrived at 5 pm, and she decided to walk in the direction Alan was coming from home. Alan had left in time to meet the 5:30 pm train, but this time he picked up Cynthia and they arrived home 10 minutes earlier
than usual.For how many minutes had Cynthia walked before Alan picked her up?
(A) 20 (B) 30 (C) 25 (D) 10 (E) 15
Could you please explain how you got 25 I'm really struggling to do this question
10 minutes early is the time that would have taken alan to drive the distance that cynthia had walked
since it is forwards and backwards
10/2
=
5
now lets think that if cynthia remained stationary and did not walk
and if she just waited
and alan drives to where she is waiting
the time would be 5:30 yes?
but because she walked
the time would be 5: 25
because the car did not have to drive that 5 minutes
and since they both start out at 5pm
the answer would be 25
Well, it seems like Cynthia decided to take some extra steps that day! Let's crunch some numbers to figure out how many minutes she walked before Alan picked her up.
Normally, Cynthia would arrive at her station at 5:30 pm, and they would get home at their usual time. But on this extraordinary day, Cynthia arrived on an earlier train at 5 pm.
Let's call the usual travel time from the station to their home "T" minutes. Since they arrived home 10 minutes earlier than usual, we can say that it took them T - 10 minutes to get home that day.
Now, here's where Cynthia's walk comes into play. She walked in the direction Alan was coming from home, so she was already making progress towards their house. By the time Alan picked her up, she had covered a portion of the distance they usually travel together.
Let's assume Cynthia walked for "W" minutes before Alan picked her up. This means that the remaining distance they covered together was T - W minutes.
Since they arrived home 10 minutes earlier than usual, we can set up an equation:
(T - W) + 10 = T
Simplifying, we have:
-T + W + 10 = 0
Rearranging, we find that W - 10 = 0, which means W = 10.
So, Cynthia walked for 10 minutes before Alan picked her up.
Therefore, the correct answer is (D) 10.
Walking can be good exercise, but let's hope Cynthia doesn't have to walk too far in the future.
To solve this problem, we need to determine the amount of time Cynthia walked before Alan picked her up.
Let's start by finding the usual travel time from the station to Cynthia's home. We know that the usual train arrives at 5:30 pm, and they arrive home afterward. Therefore, the total travel time from the train station to home is the time it takes for Cynthia to walk from the station and the time it takes for Alan to drive from the station to their home.
Since they arrived home 10 minutes earlier than usual, we can subtract 10 minutes from the usual travel time.
Now, let's calculate the time Cynthia would have spent walking if she took the usual train. Since the usual train arrives at 5:30 pm, and the earlier train arrived at 5 pm, Cynthia was on the train for 30 minutes less walking time.
Since we know that Cynthia walked some amount of time before Alan picked her up and that this walking time is the difference between the usual travel time and the shorter travel time with the earlier train, we can deduce that Cynthia walked for 30 minutes.
Therefore, the answer is (B) 30. Cynthia walked for 30 minutes before Alan picked her up.