Math Sample Problems
1. A boat travels at the rate of 8kph in still water, If it can travel a given distance upstream in 5
hours and the same distance in 3 hours, what is the rate of the current?
Let the speed of the current be x
upstream the boat will lose speed by x mph.
So the boats speed will be 8-x mph
Time taken is 5 hours
So distance traveled is rate * time
(8-x) * 5
Downstream the boat will gain speed .
So the speed will be 8+x
Distance traveled = 3*(8+x)
Since the distance upstream and donstream are same
5*(8-x)= 3*(8+x)
40-5x= 24+3x
40-24= 3x+5x
16=8x
16/8=x
x=2
Speed of the current = 2mph
2. What is the value of x-6 if 2(x-3)+5=19?
Step-by-step explanation:
We do not know the value of x so we first get the value of x:
2(x-3)+5=19
2x-6+5=19
2x-1=19
2x-1+1=19+1
2x=19+1
2x=20
x=10
Since we already know that x=10, we simply substitute the value of x to x-6
10-6=4