HELP ME WITH THI D=R=T question pleasE!?

Question

The Walker family will be attending a wedding. Betty and Harold leave a day early
and arrive in the down where the wedding will take place in 3.5 hours. Mary and
Cindy leave the morning of the wedding, drive an average of 10 mph faster than their
parents did the day before, and arrive in 3 hours. How far away was the town from
the Walker residence?
a. 165 miles
b. 180 miles
c. 60 miles
d. 210 miles
e. None of the above

Answer 1

It is D = R * T (Distance equals rate times time)...

Let D be the distance to the wedding:
Let R be the parent's rate.
Let R + 10 be the children's rate

Equation for the parents.
D = R * 3.5

Equation for the children:
D = (R + 10) * 3

Since the distance (D) is the same, you can equate these two:
R * 3.5 = (R + 10) * 3

Distribute the 3 through the parentheses:
3.5R = 3R + 30

Subtract 3R from both sides:
0.5R = 30

Multiply both sides by 2 (to cancel the 0.5 = 1/2)
R = 60

So the parents travelled at 60 mph and the children travelled at 70 mph.

Plugging it back into the original equations.
D = 3.5 (60) = 210
D = 3 (70) = 210

So you get the answer either way:
The parents drove 3.5 hours at 60 mph = 210 miles.
The children drove 3 hours at 70 mph = 210 miles.

So the distance from the house to the wedding in town is:
d. 210 miles

Answer 2

The question is misleading.
Time for distance (Betty & Harold) = 3.5 hrs?
A day till wedding = 24 hrs?
morning till wedding = 3 hrs?

let's work the reverse way.

In 3 hrs,
a. 165 miles is in 55 mph
b. 180 miles is in 60 mph
c. 60 miles is in 20 mph
d. 210 miles is in 70 mph.

Taking the question is saying that Betty & Harold takes 3.5 hrs to reach and Mary & Cindy take 3 hrs.

Thus, the ratio is 3.5:3.

Into equation,

3.5(x-10) = 3(x)
0.5 (x) = 35
(x) = 70

Thus, the distance is in 70 mph. Thus, distance is 3 x 70 = 210 miles

Otherwise,

it will be (time Betty & Harold take)(x-10) = 3(x), if the time of Betty & Harold takes is more than double of Mary & Cindy, then, the should be lesser than 2(10 mph).

Answer 3

Let 'x' mph be the speed of travel of Betty and Harold
therefore, the speed of Mary and Cindy will be (x+10) mph

And let D be the distance from the town from the Walker residence.

Speed = Distance / Time

Two equations can be formed,

for Betty and Harold,
x = D / 3.5

i.e. 3.5x=D


for Mary and Cindy ,
x+10 = D/3

i.e. 3x+30= D


Equating the two equations

3.5x = 3x + 30
0.5x = 30
x = 60

Betty and Harold was travelling at 60 mph

Since they took 3.5 hours to reach the place,
the distance is 3.5 * 60 = 210 miles

Answer : d

Answer 4

Both travel the same distance. Betty and Harold's distance is:

r(3.5)

Mary and Cindy's distance is:

(r + 10)(3)

Set them equal to find Betty and Harold's rate:

3.5r = 3r + 30
0.5r = 30
r = 60

So since Betty and Harold drove 60 mph, the distance must have been:

60mph(3.5 hours) = 210 miles, answer d

Answer 5

Looking for distance (assuming this math, not Physics)

3.5 hours travlled by B & H at X mph.

3.5 * X = B & H 's distance.

3 hours travelled by M & C at X + 10 mph (10 mph faster thatn B& H)

3 * (X+10) = M & C Distance.

Both groups went to the same place, therefore both groups travel the same distance.

M & C Distance = B & H Distance, so ...

3 * (X+10) = 3.5 * X

Solve for X!