Mathematics: Aboat traveled 153 miles downstream and back. the trip downstream took 9 hours. the trip back took 17 hours. what is the speed of the boat in the still water. what is the speed of the current?

Aboat traveled 153 miles downstream and back.

jonquil201

13.01.2022

Speed of boat in still water is 13 miles per hour and speed of current is 4 miles per hour

Solution:

Let s = the speed of the boat in still water in miles/hour

Let c = the speed of the current in miles/hour

Formula to remember:

If the speed of a boat in still water is s miles/hr and the speed of the current is c miles/hr, then:

Speed downstream = (s + c) miles per hour

Speed upstream = (s - c) miles per hour

Given:

boat traveled 153 miles downstream and back

distance for downstream = 153 miles

distance for upstream = 153 miles

time taken for downstream = 9 hours

Time taken for upstream = 17 hours

The relation between speed, distance and time is given as:

$distance = speed \times time$

For downstream:

$153 = (s + c) \times 9$

$s + c = \frac{153}{9} = 17$

s + c = 17 ------- eqn 1

For upstream:

$153 = (s - c) \times 17\\\\s - c = \frac{153}{17} = 9$

s - c = 9 ------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "s" and "c"

Add eqn 1 and eqn 2

s + c = 17

s - c = 9

(+) -------------

2s = 26

s = 13

Substitute s = 13 in eqn 1

13 + c = 17

c = 17 - 13 = 4

c = 4

Thus the speed of boat in still water is 13 miles per hour and speed of current is 4 miles per hour

0,0(0 оценок)