1. Oanh walked from her home to the grocery store at 3 mi/h and jogged home at 6 mi/h. Her total round trip was 15 minutes (1/4h). How far from Oanh's home is the grocery store? (use an equation to solve this)
Help, I am totally clueless on this.
let her time walking be t hours
then the distance she walked = 3t miles
let her time jogging back home be 1/4 - t hours
so the distance she jogged = 6(1/4 - t)
but aren't those two distances the same ?
so...
3t = 6(1/4 - t)
I am sure you can solve this for t, then sub that value back into 3t to get the distance.
Wait, I don't get it.
I solved
3t = 6 (1/4 - t)
and got 11.66666666666....
and then what do I do?
..or did I do that wrong?
3t = 6 (1/4 - t)
3t = 3/2 - 6t
9t = 3/2
t = 3/18 = 1/6
then 3t, which was the distance
= 3(1/6) = 1/2
so the distance is 1/2 mile
check:
time walking = 1/2 ÷ 3 = 1/6 hour
time jogging = 1/2 ÷ 6 = 1/12 hour
1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 hour
Oh, i see.
thank you.
To solve this problem, let's break it down step by step:
Let's suppose the distance from Oanh's home to the grocery store is "x" miles.
Step 1: Determine the time it took for Oanh to walk from her home to the grocery store.
The formula to calculate time is "time = distance/speed". So, the time it took for Oanh to walk to the grocery store is x/3 hours.
Step 2: Determine the time it took for Oanh to jog back home from the grocery store.
Using the same formula, the time it took for Oanh to jog back home is x/6 hours.
Step 3: Calculate the total time for the round trip.
Since total time is given as 1/4 hours, we can set up the equation:
Total time = Time to walk + Time to jog
1/4 = x/3 + x/6
Step 4: Solve the equation for x.
To simplify the equation, we need to find a common denominator for x/3 and x/6, which is 6x.
(6x)(1/4) = (6x)(x/3) + (6x)(x/6)
6x/4 = 2x + x
3x/2 = 3x
3x = 6x
6x - 3x = 0
3x = 0
x = 0
Step 5: Interpret the solution.
The solution x = 0 means that the distance between Oanh's home and the grocery store is zero. However, this doesn't make sense in the context of the problem since Oanh needs to travel some distance to reach the grocery store. Therefore, there is no valid solution based on the given information.
In other words, we can conclude that there is either missing or incorrect information in the problem statement, as it is not possible to determine the distance between Oanh's home and the grocery store with the given data.