A train ran for 6 minutes and 37 seconds in one mile. Another train travelled 7 minutes and 35 seconds in one mile. How long (minutes/seconds) would it take each train to travel 16 miles?
The first train travels
16(6 37/60) = 96 592/60 = 105 13/15 min = 105'52" or 1 hr 45 min 52 sec
do the other similarly
You run a mile in 7 minutes 30 seconds. How long will it take you to run m miles assuming you are running at the same amount of speed. Algebraic expressions
To find out how long each train would take to travel 16 miles, we need to calculate their rates (speed) first. We can do this by finding the time taken to cover one mile for each train.
For the first train, it runs for 6 minutes and 37 seconds to cover one mile. We can convert the time to seconds for easier calculations. There are 60 seconds in a minute, so we can convert 6 minutes to seconds by multiplying it by 60, then add the remaining 37 seconds.
6 minutes = 6 * 60 = 360 seconds
360 seconds + 37 seconds = 397 seconds
Therefore, the first train takes 397 seconds to cover one mile.
For the second train, it travels for 7 minutes and 35 seconds to cover one mile. Similar to before, we convert the time to seconds.
7 minutes = 7 * 60 = 420 seconds
420 seconds + 35 seconds = 455 seconds
So, the second train takes 455 seconds to cover one mile.
Now we can calculate their rates (speed). To do this, we divide the distance traveled (1 mile) by the time taken (in seconds) for each train.
Rate of the first train = 1 mile / 397 seconds ≈ 0.00252 miles/second
Rate of the second train = 1 mile / 455 seconds ≈ 0.00220 miles/second
Now, we can find out how long it would take each train to travel 16 miles. We can use the formula:
Time = Distance / Rate
For the first train:
Time = 16 miles / 0.00252 miles/second
Calculating the result:
Time = 16 / 0.00252 ≈ 6349.21 seconds
Converting the time back to minutes and seconds:
6349.21 seconds ≈ 105 minutes and 49.21 seconds
So, the first train would take approximately 105 minutes and 49.21 seconds to travel 16 miles.
For the second train, we follow the same procedure:
Time = 16 miles / 0.00220 miles/second
Calculating the result:
Time = 16 / 0.00220 ≈ 7272.73 seconds
Converting the time back to minutes and seconds:
7272.73 seconds ≈ 121 minutes and 12.73 seconds
Therefore, the second train would take approximately 121 minutes and 12.73 seconds to travel 16 miles.