Question

A tourist covered a journey partly by foot and partly by tonga. He walked for 90 km and rode the tonga for 10 km. He spent 4 h less on the tonga than on walking. If the tourist had reversed the times he travelled by foot and on tonga, the distances travelled on each part of the journey would be equal. How long did he ride the tonga?

Answer 1

ANSWER:  

The tourist ride the tonga for 2 hours.

SOLUTION:

Given, tourist walked for 90 km and rode the tonga for 10 km. He spent 4 h less on the tonga than on walking.  

Let the time taken to travel on foot be x. then, time taken on tonga be x – 4.

$\text { Now, speed while walking on foot }=\frac{\text {distance travelled on foot}}{\text {time taken to travel on foot}}=\frac{90}{x}$

$\text { And, speed while using tonga }=\frac{\text { distance travelled on tonga }}{\text { time taken to travel on tonga }}=\frac{10}{x-4}$

Now, If the tourist had reversed the times he travelled by foot and on tonga, the distances travelled on each part of the journey would be equal.

Distance travelled on tonga = distance travelled on foot

Speed while walking on foot x time taken = speed while using tong x time taken

$\frac{90}{x}(x-4)=\frac{10}{x-4}(x)$  [as the times are reversed]

$\frac{90(x-4)}{x}=\frac{10 x}{x-4}$

On cross-multiplication, we get

$\begin{array}{l}{90(x-4)^{2}=10 x^{2}} \\\\ {\frac{(x-4)^{2}}{x^{2}}=\frac{1}{9}} \\\\ {\left(\frac{x-4}{x}\right)^{2}=\left(\frac{1}{3}\right)^{2}} \\\\ {\frac{x-4}{x}=\frac{1}{3}}\end{array}$

3x – 12 = x

3x – x = 12

2x = 12

x = 6

So, time taken to travel on tonga is x – 4 = 6 – 4 = 2 hours.  

Hence, he ride the tonga for 2 hours.

Answer 2

Answer:

Given, tourist walked for 90 km and rode the tonga for 10 km. He spent 4 h less on the tonga than on walking.  

Let the time taken to travel on foot be x. then, time taken on tonga be x – 4.

 

Now, If the tourist had reversed the times he travelled by foot and on tonga, the distances travelled on each part of the journey would be equal.

Distance travelled on tonga = distance travelled on foot

Speed while walking on foot x time taken = speed while using tong x time taken

 [as the times are reversed

On cross-multiplication, we get

3x – 12 = x

3x – x = 12

2x = 12

x = 6

So, time taken to travel on tonga is x – 4 = 6 – 4 = 2 hours.  

Hence, he ride the tonga for 2 hours