If the subway travels and average speed of 45mph and it allows you to get to work at 8:30, when you leave your house at 7:45. One day the subway was having problems and could go 35mph. how early would you have to leave your house to make it to work on time?
at the regular speed it took 45 min or 3/4 hour
so the distance is 45*3/4 mi or 135/4 miles
at a speed of 35 mph it would take
135/4 ÷ 35 hours or .96429 hours
which would be 57.9 minutes
so just back up that time from his work start of 8:30
BTW, how would he have known that the subway was going to have a problem, and left earlier to still make it on time ??????
To figure out how early you would have to leave your house to make it to work on time when the subway is traveling at a slower speed, we can follow these steps:
Step 1: Calculate the regular travel time with the average speed of 45 mph.
To calculate the regular travel time, we need to consider the distance between your house and your workplace. Let's assume it is "X" miles.
Regular travel time = distance / speed = X miles / 45 mph = X/45 hours.
Step 2: Determine the delay caused by the slower speed.
Since the subway is traveling at 35 mph instead of the regular 45 mph, we need to calculate the extra time it would take.
Extra travel time = distance / speed difference = X miles / (45 mph - 35 mph) = X/10 hours.
Step 3: Calculate the total travel time needed to arrive on time.
To calculate the total travel time, we add the regular travel time and the extra travel time.
Total travel time = Regular travel time + Extra travel time = X/45 hours + X/10 hours.
Step 4: Calculate the time difference between the regular and slower speeds.
To find out how early you need to leave your house, we subtract the regular travel time from the total travel time. This will give us the additional time needed.
Additional time = Total travel time - Regular travel time.
Step 5: Convert the additional time from hours to minutes.
Since we are looking for the additional time needed in minutes, we can convert the additional time from hours to minutes by multiplying it by 60.
Additional time in minutes = Additional time in hours × 60.
Let's assume X = 20 miles (distance between your house and workplace).
1. Calculate the regular travel time:
Regular travel time = 20 miles / 45 mph = 0.44 hours = 26.4 minutes.
2. Calculate the extra travel time:
Extra travel time = 20 miles / (45 mph - 35 mph) = 2 hours.
3. Calculate the total travel time needed to arrive on time:
Total travel time = 0.44 hours + 2 hours = 2.44 hours = 2 hours and 26.4 minutes.
4. Calculate the time difference between the regular and slower speeds:
Additional time = 2 hours and 26.4 minutes - 0.44 hours = 2 hours and 26.4 minutes.
5. Convert the additional time from hours to minutes:
Additional time in minutes = 2 hours × 60 minutes/hour + 26.4 minutes = 146.4 minutes.
Therefore, to make it to work on time when the subway is traveling at 35 mph, you would need to leave your house 2 hours and 26.4 minutes (or approximately 2 hours and 26 minutes) earlier than your usual departure time of 7:45 AM.