A taken 3 hours more than B to walk a distance of 30km. But if A doubles his speed, he is ahead of
B by 11/2 hours. Find their original speed.
Answers
Step-by-step explanation:
⭐GIVEN :
✔Distance = 30 km
Let speed of A be = x km/h & speed of B = y km/h.
Time taken by A to cover 30 km = 30/x
[ Time = Distance /speed]
Time taken by B to cover 30 km = 30/y
30/x = 30/y + 3
30/x - 30/y = 3…………(1)
[Given : A takes 3 hours more than B to walk ]
When A doubles his speed then, time taken by A = 30/2x
[Given: time taken by B = Time taken by A + 3/2 h]
30/y = 30/2x + 3/2
30/y - 30/2x = 3/2
30/y - 15/x = 3/2 ……..(2)
Let 1/x= p and 1/y = q
so eqs 1 & 2 become ,then On adding eq 3 & 4
30p - 30q = 3……….(3)
-15p + 30q = 3/2………(4)
---------------------------
15 p = 3 + 3/2
15 p =( 6 + 3)/2 = 9/2
15p = 9/2
p = 9 /(2×15) = 3/10
p = 3/10
On Putting the value of p = 3/10 in eq 3
30p - 30q = 3
30 (3/10) - 30q = 3
9 - 30q = 3
9 - 3 = 30q
6 = 30q
q = 6/30= 1/5
1/y = q [ Let 1/y = q]
1/y = ⅕
y = 5 km/h
1/x = p [Let 1/x= p ]
1/x = 3/10
x = 10/3 km/h
so x = 10/3 km/h. & y = 5 km/h
Hence, the speed of A is 10/3 km/h & B is 5 km/h.
#Regards♥️
Answer:
Step-by-step explanation:
Let speed of A and B be x and y respectively.
According to question,
30/x=30/y+3 →(1)
When A doubles his speed
30/2x=30/y-11/2 →(2)
Subtract (2) from (1)
30/x-30/2x=3+11/2
(60-30)/2x=(6+11)/2
30/x=17
x=30/17 km/h
From (1)
17=30/y+3
30/y=14
y=15/7 km/h