Help with a math problem having to do with distance, rate and time.?

Question

A husband and a wife drive to a friend's house in separate cars leaving at the same time. How far is their friend's house if the husband drives at 35 mph and his wife drive at 45 mph and husband arrives 30 minutes after his wife?

Answer 1

Let th be the time husband spent driving, and tw time wife spent driving.
The distance they passed is the same and is equal to:
th*35=tw*45
husband needed half an hour more than wife.
th=tw+0.5
Means we can replace th with tw+0.5
(tw+0.5)*35=tw*45
35*tw+17.5=45*tw
17.5=45*tw-35*tw
17.5=10*tw
tw=1.75

So their friend's house is 1.75*45=78,75 miles away.

Answer 2

Let the friends house be x miles away.
time taken by wife to arrive=x/45
time taken by husband=x/35
x/45+30/60=x/35
x/35-x/45=1/2
45x-35x=1/2*35*45
x=1/2*35*45/10
=78.75miles

Answer 3

distance = speed x time
distance = 35 ( x +.5 ) ... .5 is the 1/5 hour longer it took
distance = 45x
35 (x + .5) = 45x
35x + 17.5 = 45x
17.5 = 10x
1.75 = x
it took 1.75 hour at 45 mph to get to the house
45 * 1.75 = 78.75 miles

Answer 4

let the distance be xmiles
time taken by wife is x/45(time = distance/speed)
similarly for man x/35
we have been given that time diff is 1/2 hrs
so x/45-x/35 =1/2
solve for x

Answer 5

Using distance=rate*time:

Let r1 be the husband's speed, t1 be the husband's time, in hours.

Let r2 be the wife's speed, r2 be the wife's time, in hours.

Then r1*t1=r2*t2, because they travel the same distance.

You know r1=35 and r2=45, and t1=t2+0.5, so substituting these into the above equation gives

35*(t2+0.5)=45*t2, so 17.5=10*t2, or t2=1.75 hours, or 1 hour and 45 minutes. t1=t2+0.5=2.25, or 2 hours and 15 minutes.

To get the distance, use r1*t1=35*2.25=78.75 miles.

Answer 6

let x=# of miles.
at 35 mph, it takes x/35 hrs
at 45 mph it takes x/45 hrs so
x/35-x/45=.5
9x-7x=.5*5*7*9=157.5
2x=157.5
x=78.75 miles.
check
78.75/35=2.25 hrs
78.75/45=1.75 hrs
2.25-1.75=.5hrs=30min

Answer 7

78.75 miles. But why did they take separate cars? Did they have a fight? Was the husband going somewhere else afterward? Do the cars only have one seat? What?

Answer 8

you're no longer seeing the wooded area for the trees. no remember if that's fifty six miles one thank you to artwork, then it may be fifty six miles to come back abode. basically considering which you return and forth at a distinctive value of velocity does not replace the gap.

Answer 9

See?? You would know the answer! But, you wanted hang with the gang!!