Jim's speedboat can travel 24 miles upstream against a 4 mph current. In the same amount of time it travels 26 miles

Mathematics

1 answer:

8_murik_8 [283]2 years ago

8 0

Answer:

speed of the boat = 100 mph

Step-by-step explanation:

Let x = speed of the boat

upstream speed = x - 4

downstream speed = x + 4

time = 24/(x - 4) = 26/(x + 4)

Cross multiply:

24(x + 4) = 26(x - 4)

24x + 96 = 26x - 104

104 + 96 = 26x - 24x

200 = 2x

x = 100 mph

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When you have a scale factor as percentage, is better to convert that percentage into a fraction by divide it by 100%. That way, it will be much easier to scale your figures.

1. The scale factor we need to apply to our rectangle is 60%. Firts, lets convert our scale factor into a fraction: $\frac{60}{100} = \frac{3}{5}$ . Next, we just need to multiply each side of our rectangle by our fraction:
length= $16( \frac{3}{5})=9.6$
width= $8( \frac{3}{5} )=4.8$
So, our new rectangle will have a length of 9.6 units and a width of 4.8 units.

2. This time the scale factor is 120%. Just as before, lets convert it into a fraction: $\frac{120}{100} = \frac{6}{5}$ , and just as before lets multiply each side of our triangle by our fraction:
base= $10( \frac{6}{5} )=12$
side= $8( \frac{6}{5} )=9.6$
So, our new isosceles triangle will have a base of 12 units and tow sides of length 9.6 units each.

3. This time the scale factor is 150%. Just as before, lets convert it into a fraction: $\frac{150}{100} = \frac{3}{2}$ , and just as before lets multiply each side of our polygon by our fraction:
$12( \frac{3}{2} )=18$
$15( \frac{3}{2} )=22.5$
$13( \frac{3}{2} )=19.5$
So, our new polygon will have a side of 12 length units, tow sides of 15 length units, and two side of 15 length units.

4. This time our factor is 75%. Just as before, lets convert it into a fraction: $\frac{75}{100} = \frac{3}{4}$ , and just as before lets multiply each side of our parallelogram by our fraction:
side= $25( \frac{3}{4} )=18.75$
So, our new parallelogram will have tow sides of length 18.75 units.