Two groups of hikers take two different routes from Camp A to Camp B. The first group leaves Camp A at 9:00 AM and takes a route that is 30 miles longer than the second group's route. The second group leaves Camp A at 1:00 PM. Their hiking speed is 2 mph slower than the first group's speed.
Both groups reach Camp B at 4:00 PM. How fast does each group hike?

first groups hiking was 6mph, second groups was 4mph.

The first group was 6mph

The second group was 4mph

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not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this