Question

Han, his sister, his dad, and his grandmother step onto a crowded bus with only 3 open seats for a 42-minute ride. They decide Han’s grandmother should sit for the entire ride. Han, his sister, and his dad take turns sitting in the remaining two seats, and Han’s dad sits 1.5 times as long as both Han and his sister. How many minutes did each one spend sitting?

Answer 1

Given :

Total number of people for ride = 4

Total number of vacant seat = 3

Total duration of journey = 42 min

Han’s dad sits 1.5 times as long as both Han and his sister

To Find :

How many minutes did each one spend sitting

Solution :

∵  Han’s grandmother should sit for the entire ride

So, one seat is capture by grand daughter

now, out of 3 seat , 2 seat vacant and, number of people to seat = 3

Let the duration for which Han's sit = h min

The duration for which sister sit = s  

The duration for which dad sit = d min

And

 dad sits 1.5 times as long as both Han and his sister

i,e   d = 1.5 h

And   d = 1.5 s

So,   d + $\dfrac{d}{1.5}$ +  $\dfrac{d}{1.5}$ = 42 × 2

Or,  1.5 d + 2 d =  42 × 2 × 1.5

Or,  3.5 d = 126

∴             d = $\dfrac{126}{3.5}$

i.e           d = 36 min

So, The time duration for  Han 's dad to sit = d = 36 min

Now, The time duration for Han = $\dfrac{36}{1.5}$ = 24 min

The time duration for Han's sister = $\dfrac{36}{1.5}$ = 24 min

Hence,

The time duration for Han 's grandmother  to sit is 36 min

The time duration for Han 's dad to sit is 36 min

The time duration for Han is 24 min

he time duration for Han's sister is 24 min    Answer