Daniel drives 30 mph to the toy store and 45 mph back home, taking the same route both ways. If the total trip took two hours, how many total miles does he drive on the round-trip from home to the store and back?
Can you please explain how to do it?
How long did he spend at the toy store?
It doesn't say
let the distance each way be x miles
time for first trip = x/30
time for return trip = x/45
x/30 + x/45 = 2
multiply by 90 , the LCD
3x + 2x = 180
5x = 180
x = 36
So the roundtrip was 72 miles
check:
time at first leg of trip = 36/30 = 1.2 hrs
time at 2nd leg of trip = 36/45 = .8 hrs
total time = 1.2+.8 hrs = 2 hrs
To find the total distance Daniel drives on the round-trip, we need to determine the distance he travels in each direction and then add them together.
Let's start by finding the time it takes for Daniel to drive to the toy store. We know that he drives at a speed of 30 mph and the distance traveled is unknown. We can use the formula:
time = distance / speed
Substituting in the known values, we have:
time to toy store = distance to toy store / 30 mph
Next, let's find the time it takes for Daniel to drive back home. We know that he drives at a speed of 45 mph and the distance traveled is also unknown. Using the same formula:
time = distance / speed
Substituting in the known values, we have:
time back home = distance back home / 45 mph
Since the total trip took two hours, we can set up an equation:
time to toy store + time back home = 2 hours
Substituting in the previously obtained equations:
(distance to toy store / 30 mph) + (distance back home / 45 mph) = 2
Now, we have two equations with two unknowns. We can solve them simultaneously to find the distances.
To simplify the equation, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 90:
90 * (distance to toy store / 30 mph) + 90 * (distance back home / 45 mph) = 2 * 90
Simplifying, we have:
3 * distance to toy store + 2 * distance back home = 180
Since the distance to the toy store and back home is the same, let's call it 'd':
3d + 2d = 180
Combining like terms, we get:
5d = 180
To solve for 'd', we divide both sides of the equation by 5:
d = 180 / 5
d = 36
Therefore, the distance from home to the toy store and back is 36 miles. Since it is a round-trip, Daniel drives a total of 36 + 36 = 72 miles.