Question

Aman is caught in an emergency situation and has to
visit another town which is 80km away in exactly 8
hours. He is not able to find any vehicle nearby so he
started moving by foot at a speed of 8km per hour.
After some time, he got a bicycle and then travelled the
rest of distance on bicycle at 16km per hour. Find the
time for which Amon travelled on foot.​

Answer 1

Answer:

Let the distance be x

Hope it helps

Answer 2

Let:−

$\tt{\implies Time\:taken\:_{(by\:foot)}=x}$

$\tt{\implies Time\: taken\:_{(by\: cycle)}=6-x}$

$\sf\large\underline\purple{Given:-}$

$\tt{\implies Total\:_{(distance)}=80km}$

$\tt{\implies Total\:_{(time)}=6hours}$

$\tt{\implies Speed\:_{(by\:foot)}=8km/h}$

$\tt{\implies Speed\:_{(by\: cycle)}=16km/h}$

$\sf\large\underline\purple{To\: Find:-}$

$\tt{\implies Distance\: covered\:_{(by\:foot)}=?}$

$\tt{\implies Distance\: covered\:_{(by\: cycle)}=?}$

$\sf\large\underline\purple{Solution:-}$

➥To calculate distance covered by foot and cycle , at first we have to assume time taken by foot be (x) and time taken by cycle be (6-x). You can see above as I assumed. After that simply by applying formula distance=speed×time. With the help of this formula you have to set up equation then find out the value of x. After that you have to find time separately then calculate it's distance separately.

$\sf\large\underline\purple{Formula\: used:-}$

$\tt\green{\implies Distance=Speed*Time}$

$\tt{\implies Covered\:_{(distance\:by\:foot)}=8*x}$

$\tt{\implies Covered\:_{(distance\:by\:cycle)}=(6-x)*16}$

➨ Now setting up equation , here:-]

$\tt{\implies Total\:_{(distance)}=Sum\: distance\:_{(foot+cycle)}}$

$\tt{\implies 80=8x+16(6-x)}$

$\tt{\implies 80=8x+96-16x}$

$\tt{\implies 80-96=8x-16x}$

$\tt{\implies -16=-8x}$

$\tt{\implies 16=8x}$

$\tt{\implies x=2}$

➨ Now calculate time ,here:-]

$\tt{\implies Time\:taken\:_{(by\:foot)}=x}$

$\tt{\implies Time\:taken\:_{(by\:foot)}=2\: hours}$

$\tt{\implies Time\: taken\:_{(by\: cycle)}=6-x}$

$\tt{\implies Time\: taken\:_{(by\: cycle)}=6-2}$

$\tt{\implies Time\: taken\:_{(by\: cycle)}=4\:hours}$

➨Now calculate distance , here:-]

$\tt{\implies Covered\:_{(distance\:by\:foot)}=8*2}$

$\tt{\implies Covered\:_{(distance\:by\:foot)}=16km}$

$\tt{\implies Covered\:_{(distance\:by\:cycle)}}$

$\tt{\implies Covered\:_{(distance\:by\:cycle)}}$

$\tt{\implies Covered\:_{(distance\:by\:cycle)}=4*16}$

$\tt{\implies Covered\:_{(distance\:by\:cycle)}}$

$\sf\large{Hence,}$

$\sf\blue{Distance\: covered\:by\:Aman\:_{(on\:foot)}=16km}$

$\sf\large\underline\purple{Verification:-}$

$\tt{\implies Total\:_{(distance)}=Sum\: distance\:_{(foot+cycle)}}$

$\tt{\implies 80=8x+16(6-x)}$

$\tt{\implies 80=8*2+16(6-2)}$

$\tt{\implies 80=16+96-32}$

$\tt{\implies 80=112-32}$

$\tt{\implies 80=80}$

$\tt{\implies Hence\:,L.H.S=R.H.S}$