Question

The family visits two waterfalls, the Humboldt Falls and the Bridal Veil Falls. The ratio of the heights Humboldt Falls : Bridal Veil Falls \[ = 5:1\]. The Humboldt Falls are \[220\]m higher than the Bridal Veil Falls. Calculate the height of the Humboldt Falls.

Answer 1

Hint: Here we solve using the ratio of two waterfalls, which will give us a relation between the Humboldt Falls and the Bridal Veil Falls and then solve the height relation between the two falls using the given ratio. * Here we use the concept of ratio which gives us a relation between two quantities i.e. If we say \[m:n = 1:2\], we mean for every \[1\] \[m\] there are \[2\] \[n\]
* Ratio \[m:n = 1:2\] can be written as \[\dfrac{m}{n} = \dfrac{1}{2}\].
* If the first quantity is given \[p\] more than the second quantity, then we add \[p\] to the second quantity then it becomes equal to the first quantity.
Say \[x\] is \[p\] more than \[y\], then we write \[x = p + y\] .

Complete step by step solution:
Given the ratio of heights of two waterfalls,
Humboldt Falls : Bridal Veil Falls \[ = 5:1\]
Denote height of Humboldt Falls by \[{x_1}\] and height of Bridal Veil Falls by \[{x_2}\].
Therefore, we can write \[\dfrac{{{x_1}}}{{{x_2}}} = \dfrac{5}{1}\]
Cross multiplying the values we get \[1 \times {x_1} = 5 \times {x_2}\]
i.e. \[{x_1} = 5{x_2}\] \[...(i)\]
Also, we have Humboldt Falls are \[220\]m higher than the Bridal Veil Falls
Therefore, Height of Humboldt Falls \[ = \] Height of Bridal Veil Falls \[ + 220\]m
i.e. \[{x_1} = 220 + {x_2}\] \[...(ii)\]
Substitute the value of \[{x_1}\] from equation \[(i)\] in equation \[(ii)\].
\[5{x_2} = 220 + {x_2}\]
Take variables on one side of the equation.
\[5{x_2} - {x_2} = 220\]
\[4{x_2} = 220\]
Dividing both sides by \[4\]
\[\dfrac{{4{x_2}}}{4} = \dfrac{{220}}{4}\]
\[{x_2} = 55\]
Therefore, the height of Bridal Veil Falls is \[55\]meters .
Now substitute the value of \[{x_2} = 55\] in equation \[(ii)\]
\[{x_1} = 220 + {x_2}\]
\[{x_1} = 220 + 55\]
\[{x_1} = 275\]

Thus, the height of Humboldt Falls is \[275\]meters.

Note:
In these questions, always write the final answer along with the unit of measurement. Students should always convert the measures in one common unit throughout the question to avoid incorrect calculations.
Some conversions for length are
\[
  1Km = 1000m \\
  1m = 100cm \\
  1cm = 10mm \\
  1Km = 0.6214miles \\
  1ft = 0.3048m \\
 \]
Where \[m\] stands for meters, \[cm\]stands for centimeters, \[Km\] stands for kilometers, \[ft\] stands for foot.