Question

A kangaroo hopped \dfrac13
3
1
​
start fraction, 1, divided by, 3, end fraction of the distance to the lake with her baby in her pouch. She hopped the remaining 7{,}0407,0407, comma, 040 yards without her baby in her pouch.

Answer 1

Given:

Kangaroo hopped $\frac{1}{3} rd$ of the distance to the lake with her baby

Remaining distance hopped by the kangaroo to the lake without her baby = 7040 yards

To find:

No. of miles the kangaroo hopped to the lake

Solution:

Let "x" yards be the total distance travelled by the kangaroo to the lake.

So, distance travlled by the kangaroo to the lake with her baby in her pouch = $\frac{x}{3}$

∴ The remaining distance travelled without her baby = $x - \frac{x}{3} = \frac{3x - x}{3} = \frac{2x}{3}$

But, it is given that she hopped 7040 yards without her baby in her pouch

∴ $\frac{2x}{3} = 7040$

⇒ $x = \frac{7040\: *\: 3}{2}$

⇒ $x = \frac{21120}{2}$

⇒ $x = 10560$ yards ← total distance travelled by the kangaroo to the lake

Now, we will convert the total distance travelled by the kangaroo in miles

We have, 1 mile = 1760 yards

(by unitary method)

∴ 10560 yards = $\frac{10560}{1760}$ = 6 miles

Thus, the kangaroo hopped 6 miles to the lake.

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