A bus leaves Denver 50 minutes before a second bus.
The first bus travels at 47 mph, and the second bus travels 60 mph.
How long does it take the 2nd bus to catch up to the first bus?
a) Let
the time the first bus spends traveling. Write the equation you would use to find this time.
b)
hours after the first bus left, the second bus catches up. (Round to one decimal place.)
c) Convert your time from b) to hours to hours and minutes:
hours and
minutes
a) Let x be the time the first bus spends traveling. The equation to find this time is:
x = (distance traveled by first bus) / (speed of first bus)
b) The second bus catches up x hours after the first bus left. To find this time, we can use the equation:
x + 50/60 = (distance traveled by second bus) / (speed of second bus)
The 50/60 is converted to hours since the second bus travels at 60 mph.
c) To convert the time from b) to hours and minutes, we can use the fact that there are 60 minutes in an hour. We can find the minutes by multiplying the decimal part of the time by 60. For example, if the time is 1.5 hours, we would have 1 hour and (0.5 * 60) = 30 minutes.
So, the time in hours and minutes would be x hours and (0.5 * 60) minutes.
a) Let t be the time the first bus spends traveling. The equation we would use to find this time is t = (50 / 60) + t, where (50 / 60) is the time in hours the second bus leaves before the first bus.
b) To find when the second bus catches up, we need to determine the time it takes for the second bus to travel the same distance as the first bus. Since the first bus travels at 47 mph and the second bus travels at 60 mph, the second bus catches up at a rate of 60 - 47 = 13 mph. Therefore, the time it takes for the second bus to catch up is t = distance / rate = distance / 13.
c) To convert the time from b) to hours and minutes, we need to divide the time in minutes by 60 and separate the result into hours and minutes.