46.3k views
0 votes
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?

User Emvidi
by
7.3k points

2 Answers

4 votes
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

User Ouma
by
6.9k points
7 votes

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.

User Thaks
by
6.9k points