Jennifer drove at steady speed for 2 hours then reduced speed by 10 mph and drove for another 3 hours what was the initial speed if the total distance was 220 miles?
2 v + 3 (v-10) = 220
5 v - 30 = 220
5 v = 250
v = 50
To solve this problem, we need to apply the concept of average speed. The average speed is given by the total distance divided by the total time taken.
Let's break down the given information:
- Jennifer drove at a steady speed for 2 hours.
- Then, she reduced her speed by 10 mph and drove for another 3 hours.
- The total distance traveled was 220 miles.
Let's calculate the average speed:
Step 1: Find the distance traveled during the first 2 hours.
To find the distance, we multiply the time by the speed:
Distance1 = Speed1 * Time1
Distance1 = Speed1 * 2
Step 2: Find the distance traveled during the next 3 hours.
Since Jennifer reduced her speed by 10 mph, we subtract 10 from the initial speed to get the new speed:
Speed2 = Speed1 - 10
Now, we can calculate the distance traveled during the next 3 hours:
Distance2 = Speed2 * Time2
Distance2 = (Speed1 - 10) * 3
Step 3: Calculate the total distance:
Total Distance = Distance1 + Distance2
Total Distance = Speed1 * 2 + (Speed1 - 10) * 3
Given that the total distance is 220 miles, we can set up the equation:
220 = Speed1 * 2 + (Speed1 - 10) * 3
Simplifying the equation:
220 = 2Speed1 + 3Speed1 - 30
Combining like terms:
220 + 30 = 5Speed1
250 = 5Speed1
Now, solve for Speed1:
Speed1 = 250 / 5
Speed1 = 50 mph
Therefore, the initial speed was 50 mph.