Problem: what type of problem is this?
Mandi drove slowly for 3 hours in a rain storm. When the skies cleared,she increased her speed by 30 mph and drove 4 more hours, completing her 295-mile trip. How fast was she driving in the rain storm?
This problem involves speed, time and distance. The key is to remember
that speed multiplied by time gives distance.
Take it step by step. We are given the total distance: 295 miles.
We are given the time for both segments of the trip, 3 hrs and 4 hrs.
We are not given either speed, but we are given speed for the second
segment relative to the speed for the first segment: x + 30.
The distance for the first segment is 3x.
The distance for the second segment is 4(x + 30).
The total distance is: 3x + 4(x + 30) = 295
From that, we can determine the speed for the first
segment of the trip.
3x + 4(x + 30) = 295 mi
7x + 120 = 295
7x = 175
x = 25 mph
We can verify that:
3 hrs * 25 mph = 75 mi
4 hrs * 55 mph = 220 mi
220 mi + 75 mi = 295 mi
Answer: she was driving 25 mph in the rain storm.