Question

Starting at home, ishaan traveled uphill to the grocery store for 121212 minutes at just 151515 mph. he then traveled back home along the same path downhill at a speed of 303030 mph. what is his average speed for the entire trip from home to the grocery store and back?

Answer 1

The average speed is defined as the total distance covered divided by the time interval.

First of all we need to convert the time interval from minutes to hours, so:


`121212min((1h)/(60min)) = 2020.2h`

We know that the distance, speed and time are related as follows:


`d = vt`

Thus, the distance covered from home to the grocery store is:


`d = 151515(2020.2)=306090603mi`

So, the total distance covered for the entire trip from home to the grocery store and back is:


`d_(t) = 2(306090603) = 612181206mi`

We need to the total time interval, that is:


`t = t_(1) + t_(2) = 2020.2h + t_(2)`

So, it is necessary to find
`t_(2)` as:


`t_(2) = (306090603mi)/(303030mph) = 1010.1h`

In this way:


`t = 2020.2h + 1010.1h = 3030.3h`

Finally, his average speed for the entire trip from home to the grocery store and back is:


`v_(a) = (d_(t))/(t) = (612181206mi)/(3030.3h) = 202020,ph`

Answer 2

Answer: The average speed for the entire trip from home to the grocery store and back is 20 mph.

Explanation:

Since we have given that

Ishan traveled uphill to the grocery store for 12 minutes at just 15 mph.

So, Time taken by him = 12 minutes

Speed = 15 mph

So, distance traveled = Speed × time

So, Distance becomes
`15* (12)/(60)=(180)/(60)=3\ miles`

Again, he traveled back home along the same path downhill = 180 miles

Speed of covering downhill = 30 mph

so, Time taken
`(Distance)/(Speed)=(3)/(30)=(1)/(10)\ hours`

Since we know the formula for "Average speed ":

`(Total\ distance)/(Total\ Time)\\\\\\=(3+3)/((12)/(60)+(1)/(10))\\\\\\=(6)/((1)/(5)+(1)/(10))\\\\\\=(6* 10)/(2+1)\\\\\\=(6* 10)/(3)\\\\\\=20\ mph`

Hence, the average speed for the entire trip from home to the grocery store and back is 20 mph.