Both the bus and the motorcycle are driving opposite to each other.
From the given data, the time at which both the bus and the motorcycle will pass each other is 3:25 PM
Given that:
- Distance between New Orleans and Houston = 353 miles.
- Bus leaves Houston for New Orleans at 12:20 PM.
- Speed of bus = 60 mph
- After 45 minutes, the motorcycle leaves New Orleans for Houston at 72 mph.
To find:
The time at which both the motorcycle and the bus will pass each other.
Calculations:
Let after t hour from the time when motorcycle starts, they both meet.
Then we have:
353 miles = 45 minute traveled by bus + distance traveled by bus in t hour + distance traveled by motorcycle in t time.
Since 45 minutes is three fourth of an hour, thus:
Distance traveled by bus in 45 minutes is calculated as:
[tex]D_{Bus}(45 \:\rm min) = 60 \times \dfrac{3}{4} \: \rm miles = 45 \: \rm miles[/tex]
Distance traveled by bus in t hours is:
[tex]D_{Bus}(t \: \rm hours) = 60 \times t \: \rm miles = 60t \: \rm miles[/tex]
Distance traveled by motorcycle in t hour is:
[tex]D_{motorcycle}(t \: \rm hours) = 72 \times t \: \rm miles = 72t \: \rm miles.[/tex]
Thus, we have:
[tex]353 = 60t + 72t + 45\\\\308= 132t\\\\t = \dfrac{308}{132}\\\\t= \dfrac{7}{3}\: \rm hours\\\\t=2 \: \rm hours + 20 \: \rm minutes[/tex]
Thus, time at which they meet was 12:20 PM + 45 minutes + 2 hours + 20 minutes = 3:25 PM
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