Question

Aman is caught in an emergency and has to visit
another town 80 km away in exactly 6 hours. He
cannot 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 the distance
on a bicycle at 16km per hour. Find the distance
travelled by Aman on foot.​

Answer 1

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

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

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

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

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

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

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

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

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

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

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

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

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:-]

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

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

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

$\tt{\implies Covered\:_{(distance\:by\:cycle)}=(6-2)*16}$

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

$\tt{\implies Covered\:_{(distance\:by\:cycle)}=64km}$

$\sf\large{Hence,}$

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

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

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

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

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

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

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

$\tt{\implies 80=80}$

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

Answer 2

${\large{\bold{\rm{\underline{Correct \; question}}}}}$

★ Aman is caught in an emergency and has to visit another town 80 km away in exactly 6 hours. He cannot find any vehicle nearby, so he started moving by foot at a speed of 8 km per hour. After some time, he got a bicycle and then travelled the rest of the distance on a bicycle at 16 km per hour. Find the distance travelled by Aman on foot.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

✠ *Aman is caught in an emergency and has to visit another town*

↝ Town is 80 km away in exactly 6 hours.

$\; \; \; \; \; \; \; \; \; \;{\bf{In \: short, \: means}}$

➛ Total distance = 80 km

➛ Time taken = 6 hours

✠ *He cannot find any vehicle nearby, so he started moving by foot*

↝ Speed = 8 km/h moving via foot.

$\; \; \; \; \; \; \; \; \; \;{\bf{In \: short, \: means}}$

➛ Speed(foot) = 8 km/h

✠ *After some time, he got a bicycle and then travelled*

↝ The rest of the distance he traveled on a bicycle at 16 km/h

$\; \; \; \; \; \; \; \; \; \;{\bf{In \: short, \: means}}$

➛ Speed(bicycle) = 16 km/h

${\large{\bold{\rm{\underline{To \; find}}}}}$

✯ The distance travelled by Aman on foot.

${\large{\bold{\rm{\underline{Solution}}}}}$

✯ The distance travelled by Aman on foot = 16 kilometres

${\large{\bold{\rm{\underline{Assumptions}}}}}$

✯ Time taken(foot) = a

✯ Time taken(bicycle) = 6-a

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

✯ Formula to find distance

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

✯ Distance = Speed × Time

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

________________________

~ As we already taked a view on the question and we already understand that what is given here. But let me tell you in short, it is given that a boy Aman have to go 80 km in exactly 6 hrs and he travelled 8 km/h by foot then 16 km/h via bicycle then this question says that we have to find the distance travelled by Aman on foot. We have use formula to find distance. And have to put value according to formula and have to use assumptions. Let's solve this..!

➙ Distance(foot) = 8 × a

➙ Distance(bicycle) = (6-a) × 16

~ The formed equation is,

➙ Total Distance = Sum of distance means of foot and the bicycle

➙ 80 = 8a + 16(6-a)

➙ 80 = 8a + 96 - 16a

➙ 80 - 96 = 8a - 16a

➙ -16 = -8a

➙ 16 = 8a

➙ 16/8 = a

➙ 2 = a

➙ a = 2

________________________

~ Now let's find the time taken,

➙ Time taken(foot) = 2 hrs

➙ Time taken(bicycle) = 6 - a

➙ Time taken(bicycle) = 6 - 2

➙ Time taken(bicycle) = 4 hrs

________________________

~ Now let's calculate the distance,

➙ Distance via foot = 8 × 2

➙ Distance via foot = 16 kms

________________________