Let's first determine the travel times for both Henry and Joe.
Henry leaves his house at 1:00 PM and arrives at the river at 4:30 PM. The time taken by Henry is:
4:30 PM - 1:00 PM = 3 hours and 30 minutes = 3.5 hours.
Joe leaves at the same time (1:00 PM) and arrives at the desert at 3:30 PM. The time taken by Joe is:
3:30 PM - 1:00 PM = 2 hours and 30 minutes = 2.5 hours.
Now, since we know the total distance between the river and the desert is 360 miles, we can set up the equation based on their equal speeds.
Let \( r \) be the rate of travel (in miles per hour) for both of them. The distance traveled by Henry can be represented as:
\[ \text{Distance by Henry} = r \times 3.5 \]
The distance traveled by Joe can be represented as:
\[ \text{Distance by Joe} = r \times 2.5 \]
Since the total distance between the river and the desert is 360 miles, we can write:
\[ \text{Distance by Henry} + \text{Distance by Joe} = 360 \]
Substituting the distances gives:
\[ r \times 3.5 + r \times 2.5 = 360 \]
Combining like terms:
\[ r(3.5 + 2.5) = 360 \]
This simplifies to:
\[ r(6) = 360 \]
Now, solving for \( r \):
\[ r = \frac{360}{6} = 60 \]
Thus, the rate of travel for both Henry and Joe is:
\[ \boxed{60} \text{ miles per hour.} \]
1 answer