Billye ran to town at 8 kilometers per hour and then walked back home at 3 kilometers per hour. How far was it to town if the round trip took 11 hours?
I still don't understand . . . is it x/24 that equals 1? . . . . Does that mean x=24?
Let X be the distance.
Time = Distance/Speed
X/8 + X/3 = 11 hours
Convert to a common denomimator.
(3X + 8X)/24 = 11
11 X /24 = 11
Divide both sides by 11.
X/24 = 1
Do you see where to go from here?
To find the distance to town, we can use the formula: Distance = Speed × Time.
Let's call the distance to town "d" kilometers.
Billye's speed while running to town is 8 kilometers per hour, so the time taken for this part of the trip can be calculated as: Time taken = Distance / Speed = d / 8 hours.
On the way back home, Billye walks at a speed of 3 kilometers per hour. So the time taken for this part of the trip can be calculated as: Time taken = Distance / Speed = d / 3 hours.
The total time of the round trip is given as 11 hours.
Now we can set up the equation:
d / 8 + d / 3 = 11.
To solve this equation, we need to first find a common denominator for the fractions. The least common multiple (LCM) of 8 and 3 is 24.
Multiplying both sides of the equation by 24, we get:
3d + 8d = 11 × 24.
Combining like terms, we obtain:
11d = 264.
Finally, dividing both sides of the equation by 11 gives us:
d = 24.
Therefore, the distance to town is 24 kilometers.