Ben traveled by car at an average speed of 29 miles per hour.
Then, he traveled by motorcycle at an average speed of 53 miles per hour.
In total, he traveled 333 miles for 9 hours.
How many minutes did Ben travel by motorcycle? (Round to the nearest minute.)
if he traveled x miles at 29 m/h and y miles at 53 m/h, then
x+y=333 and, since time = distance/speed,
x/29 + y/53 = 9
so,
x/29 + (333-x)/53 = 9
x = 174
y = 159
check:
174+159 = 333
174/29 + 159/53 = 6+3 = 9
but how to calculate this part with x/29+(333-x)/53=9
?
To find out how many minutes Ben traveled by motorcycle, we need to first determine how long he traveled by car. We have the total distance traveled and the average speed of the car, so we can use the formula:
Time = Distance / Speed.
Let's calculate the time spent traveling by car:
Distance traveled = Total distance - Distance traveled by motorcycle
Distance traveled by motorcycle = 333 miles
Total distance = 333 miles
Therefore, Distance traveled by car = Total distance - Distance traveled by motorcycle
= 333 miles - 333 miles
= 0 miles.
Since the distance traveled by car is 0 miles, it means Ben didn't spend any time traveling by car.
Now, let's find the time spent traveling by motorcycle. We have the average speed of the motorcycle and the total time taken for the entire trip. Using the same formula as before, we can calculate the time spent traveling by motorcycle:
Time = Distance / Speed.
Distance traveled by motorcycle = Total distance
Total distance = 333 miles
Average speed of the motorcycle = 53 miles per hour
Time spent traveling by motorcycle = Distance traveled by motorcycle / Average speed of the motorcycle
= 333 miles / 53 miles per hour
≈ 6.28 hours.
To convert hours to minutes, we can multiply by 60:
Time spent traveling by motorcycle in minutes = 6.28 hours * 60 minutes per hour
≈ 377 minutes.
Rounding to the nearest minute, Ben traveled by motorcycle for approximately 377 minutes.