If 2 bikers had to bike 200km. One was 5km/h faster than the other...?

Question

If 2 bikers had to bike 200km. One was 5km/h faster than the other and that person also made a 30min stop on the way to the finish. They both crossed the finish line at the same time. How would I go about completing this question? All i can get is (a=b+5) with "a" being the first biker and "b" being the second biker

Answer 1

OK
Now time taken by the first biker to travel 200 km is 200/(a+5) +1/2 (taken as rest) hrs.
and the time taken by the second biker to travel the same distance is 200/a
By the problem.
200/(a+5) +1/2=200/a
Now solving the equation you get your answer
200/(a+5) +1/2=200/a
or,(400+a+5)/2a+10=200/a
or,400a+a^2+5a=400a+2000 [by cross-multiplication]
or,a^2+5a-2000=0
or a={-5+-sqrt(25+8000)}/2
=(-5+-89.58)/2
rejecting the negative value of a.we get
a=42.29
Therefore the speed of the second biker was 42.29kmph and that of the first one was 47.29 kmph

Answer 2

You need to find out the time required for them to reach the finish line, I assume. The distance is 200 km. The speed can be found by taking distance divided by time, so this becomes
speed=200/time.

Since one biker was 5 kph faster than the other, but stopped for 30 minutes, we can write this situation out like this, if speed is the speed of the slower biker and time is the time it took both bikers to reach the finish line:

speed+5=200/(time-30)

speed+5 represents that the faster biker was 5 kph faster than the slower biker, and time-30 represents that the biker should have gotten there 30 minutes sooner than he did. For the slower biker, the relation is simpler:

speed=200/time

This sets up a system of equations, which we can use to solve for the time required.

speed+5=200/(time-30)
speed=200/time

(200/time)+5=200/(time-30)

Use these relations to solve for whatever information you need from the problem.

Answer 3

biker A rode at x km/hr.
biker B rode at (x+5) km/hr

Biker A reached the destination in 200 km/( x km/hr) = 200/x hrs.
Biker B reached the destination in 200/(x+5) hrs + 1/2 hr stop.

200/x = 200/(x+5) + .5
Multiply everything by (x)(x+5)
200(x+5) = 200x + 5x(x+5)
200x + 1000 = 200x +5x^2 +25x
0 = 5x^2 + 25x - 1000
0 = x^2 +5x - 200
Do the quadratic and find the positive answer for x

Answer 4

Try this, where
t= time in motion (total time to finish is the same, but biker "a" stopped for 30 minutes, so his time is motion is less. t(b) is how long it took them to get to the finish line.)

v= velocity while in motion

x= distance traveled

t(a) = t(b) - 30 min
v(a) = v(b) + 5km/hr
x(a) = x(b) = 200 km

v(a) = x(a)/t(a)
v(b) = x(b)/t(b)

Substitute. There may be an easier way, this is what readily comes to mind.

Answer 5

let them reach the crossing line in t hours
200/t=200/(t-1/2)-5
40/t=40/(t-1/2)-1
40[1/t-1/(t-1/2)]=-20/t(t-1/2=-1
t(t-1/2=20
t(2t-1)=40
2t^2-t-40=0

t-1/2

Answer 6

You didn't give what is required for the answer. I'll work on it anyway tho...