Question

A person walked at a speed of 9km/h to taxi stand and then took taxi , which travelled at a speed of 12.5m/sec If he reached his office 28km away in 48minutes Find the distance between his home and taxi stand and also the time taken to cover this distance

Answer 1

subtract the minutes and then calculate the distance between the home and the office thank u

Answer 2

Answer:

The distance from home to taxi stand is 2.07 km in 0.23 hours.

Step-by-step explanation:

Given : A person walked at a speed of 9 km/h to taxi stand and then took taxi, which traveled at a speed of 12.5 m/sec If he reached his office 28 km away in 48 minutes.

To Find : The distance between his home and taxi stand and also the time taken to cover this distance ?

Solution :

Let the distance covered by person in walking is $d_1$

Speed of the person is $s=9\ km/hr$

Time taken in walking is $t_1$

According to relationship between them,

$d_1=9t_1$ .....(1)

Let the distance covered by person in taxi is $d_2$

Speed of the person is $s=12.5\ m/s$

Convert km/hr into m/s,

$s=12.5\times \frac{18}{5}=45\ km/hr$

Time taken in walking is $t_2$

According to relationship between them,

$d_2=45t_2$ .....(2)

If he reached his office 28 km away in 48 minutes.

i.e. $d_1+d_2=28$

Substitute the values,

$9t_1+45t_2=28$ ...(3)

Converting minutes into hours,

48 minutes = 0.8 hours

and $t_1+t_2=0.8$ ....(4)

Solving (3) and (4) by multiplying (4) by 9 and subtract from (3),

$9t_1+45t_2-9t_1-9t_2=28-7.2$

$36t_2=20.8$

$t_2=\frac{20.8}{36}$

$t_2=0.57$

Substitute in (4),

$t_1+0.57=0.8$

$t_1=0.8-0.57$

$t_1=0.23$

Substitute the value of $t_1$ in (1),

$d_1=9(0.23)$

$d_1=2.07$

The distance from home to taxi stand is 2.07 km in 0.23 hours.

Substitute the value of $t_2$ in (2),

$d_2=45(0.57)$

$d_2=25.65$

The distance from taxi to office is 25.65 km in 0.57 hours.