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kolbaska11 [484]
4 years ago
8

The boat travels x miles per hour from one island to another island in 2.5 hours. The boat travels 5 miles per hour faster on th

e return trip of 2 hours. What is the distance between the island?
Mathematics
1 answer:
notka56 [123]4 years ago
6 0
The speed to the island is x. The speed to return is x+5.

The distance is the same so, 2.5 multiplied by x = 2×(x+5).

It took 2.5 hrs to get there and 2 hrs to return. Now all we have to do is solve.

 2.5*x = 2x + 10

 .5x = 10
x=20

 Therefore, the distance between islands is 2.5 × 20 = 50 miles.

hope this helps!

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In the right-angled triangle ACM, we have

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AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)

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CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)

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5x-1=7x^2-1\\\\\Rightarrow 5x=7x^2\\\\\Rightarrow x=\dfrac{5}{7},~\textup{since }x\neq 0.

Thus,

AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.

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