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Relative Speed

Problem#1

A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?

Problem#2
Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?

Problem#3
Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

Problem#4
Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.

Solution Preview

1

Let him initially make the grid of size 'x'

we have x^2 + 24 = total character used

also, (x+1)^2 - 25 = total character used

x^2 + 24 = (x+1)^2 - 25

(x+1+x)(x+1-x) = 49

2x+ 1 = 49

x = 24

total character ...

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