a motorist took 2 hours to travel from the one town to another and one hour 40 minutes to travel back calculate the percentage change in the speed of the motorist
Let's denote the distance between the two towns as D, and the speed of the motorist as S.
We know that:
- Time taken to travel from one town to another = 2 hours
- Time taken to travel back = 1 hour 40 minutes = 1.67 hours
Using the formula:
- Distance = Speed x Time
We can write:
- D = S x 2 (for the first trip)
- D = S x 1.67 (for the return trip)
Equating these two expressions for D, we get:
- S x 2 = S x 1.67
Dividing both sides by S, we get:
- 2 = 1.67
This is obviously not true, indicating there must be an error in our calculation.
Upon closer inspection, we can see that we made a mistake in equating the two expressions for D. The distance traveled during the first trip is not necessarily the same as the distance traveled during the return trip.
Let's instead assume that the distance between the two towns is the same for both trips. In other words:
- D = S1 x T1 = S2 x T2
where S1 is the speed during the first trip (from one town to another), T1 is the time taken for the first trip, S2 is the speed during the return trip (from the second town back to the first), and T2 is the time taken for the return trip.
We know that:
- T1 = 2 hours
- T2 = 1 hour 40 minutes = 1.67 hours
So:
- D = S1 x 2
- D = S2 x 1.67
Dividing the second equation by the first, we get:
- S2/S1 = 2/1.67
Simplifying, we get:
- S2/S1 ≈ 1.197
To find the percentage change in speed:
- Percentage change = (New Value - Old Value) / Old Value x 100%
Let's take S2 as the new value and S1 as the old value.
- Percentage change = (S2 - S1) / S1 x 100%
- Percentage change = (1.197S1 - S1) / S1 x 100%
- Percentage change = 0.197S1 / S1 x 100%
- Percentage change = 19.7%
Therefore, the percentage change in the speed of the motorist is approximately 19.7%.