math & speed question?

Question

a cyclist, riding steadily from his hometown, reached his destination in 4 1/2 hours. he would have taken 45 minutes less time if he had ridden his bicycle at a speed faster by 3 km/h. find the distance from his hometown to his destination. & also, tell me every step you did to get to the answer. thanks.

Answer 1

Journey _____Time(h)____speed(km/h)
__1_________4½ ______ (d / 4½)
__2_________3¾_______(d /4½)+ 3

(4½) (d / 4½) = (3¾) [ (d / 4½) + 3 ]
d = (15/4) (d) (2/9) + 45/4
36 d = 30d + 405
6d = 405
d = 405 / 6 km
d = 67 ½ km

Answer 2

{(4 1/2)*x}/(x + 3) = (4 1/2) -- 45/60
Or (4 1/2)x = (4 1/2)(x + 3) -- (45/60)(x + 3)
Or 3x/4 = 3*(4 1/2 -- 45/60)
Or x = 4/3*3*15/4 = 15 km/h
distance = (4 1/2)*15 km = 67 1/2 km

Answer 3

assume the distance is d and his speed was v

the first statement tells you d=4.5v

the second statement tells you that d=(v+3)(3.75)

you now have two equations with two unknowns, so you can solve for them. if you go to the first equation and set v=d/4.5, and substitute this into the second equation, you get:

d=(d/4.5 + 3)(3.75) or
d=0.833d + 11.25
0.1666d=11.25 or d=67.5 km and the speed was 15 km/hr

if he traveled at 18 km/hr, he would cover a distance of 67.5 km in 3.75 hours (which is 3/4 less than 4.5 hrs)

Answer 4

let S= speed in km/hr for the 4 1/2 hr trip
4.5-.75= 3.75
let S+3= speed in km/hr or the 3 3/4 hr trip

distance= speed x time = 4.5S
distance= speed x time = 3.75.(s+3)
the distance is the same therefore

4.5S= (3.75) (S+3)
4.5s=3.75s + 11.25
.75S = 11.25
S= 11.25/ .75= 15 KM/hr
4.5 x 15 = 67.5 KM
3.75 x 18 = 67.5 km
the trip is 67.5 km long

Answer 5

Given that
distance = speed*time you have
4.5*v = (4.5 - 0,75) * (v-3)
0.75 0 45 hours
This equation will give you v once you have v you can compute distance with 4.5*v