A truck leaves a depot at 11 A.M. and travels at a speed of 54 mph. At noon, a van leaves the same place and travels the same route at a speed of 64 mph. At what time does the van overtake the truck?
let the time form 11:00 to the time of overtaking be t hrs
distance gone by the truck = 54t
distance gone by the van = 64(t-1)
but they went the same distance, so ...
54t = 64(t-1)
solve for t, and add it to 11:00
2:10 is the answer our teacher taught us that
To find out at what time the van overtakes the truck, we need to determine the time it takes for the van to cover the same distance that the truck has already covered.
Let's first calculate the distance the truck has covered in 1 hour:
Distance = Speed × Time
Distance = 54 mph × 1 hour
Distance = 54 miles
So, after 1 hour (at noon), the truck has covered 54 miles.
Now, we need to find out how much time the van takes to cover the same 54 miles.
Using the formula Distance = Speed × Time, we can solve for time:
Time = Distance / Speed
Time = 54 miles / 64 mph
Calculating the time:
Time = 0.84375 hours
Now, we need to convert the decimal part of the time into minutes. There are 60 minutes in an hour. So, multiply the decimal part of the time by 60:
Minutes = 0.84375 hours × 60 minutes/hour
Minutes = 50.625 minutes
Rounding up to the nearest minute, we get:
Minutes = 51 minutes
Therefore, it will take approximately 50 minutes and 51 seconds for the van to overtake the truck.
Now, adding the time it took from noon (when the van started) to when it overtakes the truck (50 minutes and 51 seconds), we can determine the time at which the van overtakes the truck:
Time = 12:00 PM (noon) + 50 minutes + 51 seconds
So, the van overtakes the truck at approximately 12:51 PM and 51 seconds.