A man having ten hours at his disposal made an excursion, riding out at the rate of 10 miles an hour and returning on foot, at the rate of 3 miles an hour.
Find the distance he rode.
since time = distance/speed,
x/10 + x/3 = 10
To find the distance the man rode, we need to determine how long he spent riding and how long he spent returning on foot. Since the total time he had at his disposal was 10 hours, we can set up an equation to represent this:
Let x be the time (in hours) he spent riding a bicycle.
Then, 10 - x would be the time (in hours) he spent returning on foot.
Now, let's use the formula:
Distance = Speed × Time
For the riding portion, the distance he rode is:
Distance_ride = 10 miles/hour × x hours
For the returning portion, the distance he covered on foot is:
Distance_return = 3 miles/hour × (10 - x) hours
Since we want to find the total distance he rode, we can add the two distances together:
Total_distance = Distance_ride + Distance_return
Total_distance = 10x + 3(10 - x)
Total_distance = 10x + 30 - 3x
Total_distance = 7x + 30
To solve for x, we need to set up another equation using the fact that the man had 10 hours at his disposal:
x + (10 - x) = 10
Simplifying:
x + 10 - x = 10
10 = 10
Since this equation is true for any value, it means that x can be any number from 0 to 10. Thus, the man could have spent any amount of time riding between 0 and 10 hours.
However, we're interested in finding the distance he rode, not the time. To find that, we can substitute in the value of x into the Total_distance equation:
Total_distance = 7x + 30
Total_distance = 7(10) + 30
Total_distance = 70 + 30
Total_distance = 100 miles
Therefore, the man rode a distance of 100 miles.