george drove to two town at 60 miles per hour and drove back home at 30 miles per hour. what is the distance to town if the whole trip took 9 hours hrs
180 miles
time to get there = d/60
time to get back = d/30
so
d/60 + d/30 = 9
3 d/60 = 9
d = 3 * 60
Let's assume the distance from George's home to the first town is x miles.
Since George drove to the first town at 60 miles per hour, the time taken for this part of the trip can be calculated using the formula: time = distance / speed.
Therefore, the time taken to reach the first town is x miles / 60 mph.
George drove back home from the first town at 30 miles per hour, so the time taken for this part of the trip can be calculated as: time = distance / speed.
The time taken to return home is also x miles / 30 mph.
Since the whole trip took 9 hours, we can add the time taken to reach the first town and the time taken to return home together:
x/60 + x/30 = 9
To solve this equation, we can multiply each term by 60 to get rid of the denominators:
x + 2x = 540
Combining like terms gives:
3x = 540
Divide both sides of the equation by 3 to solve for x:
x = 540/3
x = 180
Therefore, the distance from George's home to the first town is 180 miles.
To find the distance to the town, we can use the formula:
distance = speed × time
Let's break down the given information:
George drove to two towns at 60 miles per hour - let's call this distance "x".
George drove back home at 30 miles per hour - the same distance of "x".
Now, let's calculate the time it took for each leg of the trip:
Time to the town = Distance / Speed
Time back home = Distance / Speed
Based on the given information, we know that the total trip took 9 hours. Therefore, the time spent going to the town and coming back home must sum up to 9 hours.
Time to the town + Time back home = 9 hours
Distance / 60 + Distance / 30 = 9
Now, we can solve this equation to find the distance:
(2 * Distance) / 60 = 9
2 * Distance = 540
Distance = 540 / 2
Distance = 270 miles
So, the distance to the town is 270 miles.