Question

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

Answer 1

Answer:

Distance between his home and taxi stand is 2 km

The time taken to cover this distance between home and taxi stand is 800 sec

Step-by-step explanation:

Time taken for walikng  is $t_{1}$

Time taken for taxi is $t_{2}$

Speed of walking is $v_{1}=9 km/hr =9\frac{1000}{3600} =2.5 m/s$

Speed of taxi is $v_{2}=12.5 m/s$

Total time taken is $t_{1}+t_{2}=48 min =48\times 60=2880 sec$..................(1)

Total distance traveled is $2.5 t_{1}+12.5t_{2}=28 km =28 \times 1000= 28000 m$..........(2)

From equation 1, $t_{2}=2880-t_{1}$

substitute this value in equation 2, we get

$2.5 t_{1}+12.5(2880-t_{1})=28000\\-10t_{1}=288000-36000\\10t_{1}=8000\\t_{1}=800 sec$

The time taken to cover this distance between home and taxi stand is 800 sec

Distance between his home and taxi stand  is $800\times 2.5 =2000 m =2 km$

Answer 2

Answer:

Distance between his home and taxi stand is 2 km

The time taken to cover this distance between home and taxi stand is 800 sec

Step-by-step explanation:

Time taken for walikng is t_{1}t

1

Time taken for taxi is t_{2}t

2

Speed of walking is v_{1}=9 km/hr =9\frac{1000}{3600} =2.5 m/sv

1

=9km/hr=9

3600

1000

=2.5m/s

Speed of taxi is v_{2}=12.5 m/sv

2

=12.5m/s

Total time taken is \begin{gathered}t_{1}+t_{2}=48 min =48\times 60=2880 sec\\\end{gathered}

t

1

+t

2

=48min=48×60=2880sec

..................(1)

Total distance traveled is 2.5 t_{1}+12.5t_{2}=28 km =28 \times 1000= 28000 m2.5t

1

+12.5t

2

=28km=28×1000=28000m ..........(2)

From equation 1, t_{2}=2880-t_{1}t

2

=2880−t

1

substitute this value in equation 2, we get

\begin{gathered}2.5 t_{1}+12.5(2880-t_{1})=28000\\-10t_{1}=288000-36000\\10t_{1}=8000\\t_{1}=800 sec\end{gathered}

2.5t

1

+12.5(2880−t

1

)=28000

−10t

1

=288000−36000

10t

1

=8000

t

1

=800sec

The time taken to cover this distance between home and taxi stand is 800 sec

Distance between his home and taxi stand is 800\times 2.5 =2000 m =2 km800×2.5=2000m=2km