Question

While driving from​ Chicago, Brent had a visibility problem due to the fog. After 1 1/2

​hours, the fog lifted and he was able to increase his speed by 44 ​mph, driving another 2 and 1/2 hours. If the entire trip was 206 ​miles, how fast was he traveling in the​ fog?

Brents rate of speed in the fog was ____mph.



Two Snails are 391 centimeters apart. They crawl toward each other at rates that differ by 1 ​cm/min. After 23 ​minutes, they meet. How fast is each snail​ crawling?
The Slower snail is moving at ____cm/min.
The faster snail is moving at ___cm/min.


Two crews are laying blacktop on a road. They start at the same time at opposite ends of a 8​-mile road and work toward one another. One crew lays blacktop at an average rate of 0.5 mile a day faster than the other crew. If the two crews meet after 3.2 ​days, find the rate of each crew.

The rate of the faster crew is ____ miles per day.
The rate of the slower crew is ____ miles per day.

Answer 1

1) Let x be the original speed that he was driving;

x mph ---> 1.5 hours
x+44 mph --> 2.5 hours

1.5x + 2.5(x+44)=206
1.5x+2.5x+110=206
4x=206-110
4x=96
x=24
Therefore, he was travelling at 24 mph in the fog.

2) Let x be the speed of 1 snail,
The other snail travels at the speed of x+1 cm/min

23x+23(x+1)=391 <-- solve for x
23x+23x+23=391
46x=368
x=368/46
x=8

Therefore one of the snail travels at 8 cm/min while the other goes at 9 cm/min

7) Let x be one crew
Then the other crew would be working at x+0.5

3.2x+3.2(x0.5)=8 <-- solve for x
3.2x+1.6x=8
4.8x=8
x=8/4.8
x=1.6666 or 1.7 miles

Therefore, one of the crew does 1.7 miles per day and the other crew does (0.5*1.7)=0.85 miles

Hope I helped :)