Tim and Rich are racing up a 25-foot wall. Tim climbs at 8 inches per minute and Rich climbs at 10 inches per minute. If Tim has a 5 minute head start, by how many SECONDS does the winner beat the other?
25 feet is 300 inches
Tim has a 40 inch head start
... it takes him ... (260 / 8) minutes to reach the top
it takes Rich ... (300 / 10) minutes to reach the top
To find out by how many seconds the winner beats the other, we need to first determine the time taken by each person to climb the wall. We can then compare the times and calculate the difference.
Let's start with Tim's time to climb the wall. Tim has a 5-minute head start, so he climbs the wall for a total duration of (5 minutes + Tim's climbing time). Since Tim climbs at a rate of 8 inches per minute, we need to convert the wall's height of 25 feet into inches, which is 25 * 12 = 300 inches.
To find Tim's climbing time, we divide the total distance climbed (300 inches) by his climbing speed (8 inches per minute):
Time taken by Tim = Distance / Speed = 300 inches / 8 inches per minute
Simplifying the equation, we get:
Time taken by Tim = 37.5 minutes
Now, let's calculate Rich's climbing time. Since Rich does not have a head start, his climbing time is simply the total distance climbed (300 inches) divided by his climbing speed (10 inches per minute):
Time taken by Rich = Distance / Speed = 300 inches / 10 inches per minute
Simplifying the equation, we find:
Time taken by Rich = 30 minutes
We can see that Rich climbs the wall faster than Tim. Now, to find the difference in seconds, we calculate the time difference between the two:
Time difference = Time taken by Tim - Time taken by Rich = 37.5 minutes - 30 minutes
Since we want the answer in seconds, we convert the minutes into seconds:
Time difference = (37.5 minutes - 30 minutes) * 60 seconds/minute
Simplifying the equation, we find:
Time difference = 450 seconds - 1800 seconds
The time difference between the winner and the other is:
Time difference = -1350 seconds
However, since the question asks by how many seconds the "winner" beat the other, we discard the negative sign:
Time difference = 1350 seconds
Therefore, the winner beats the other person by 1350 seconds.