\(d=rt\), where \(d\) is the distance covered, \(r\) rate and \(t\) time. Question: \(t=?\)

(1) \(r=72\). Clearly not sufficient.
(2) \((r+8)(t-1)=d\). Clearly not sufficient.

(1)+(2) \(r=72\) and \((r+8)(t-1)=d\) --> \(80(t-1)=d\) --> \(d=80(t-1)=rt=72t\) --> \(8t=80\) --> \(t=10\). Sufficient.

Answer: C.
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1: Not sufficient, easy to spot
2: distance is d
av speed: a then time is t
av speed: a-1 then time is t-1
d/a = d/a+8 + 1 can't solve alone insufficient.

Combining, d/72 = d/80 + 1 solving d = 80 then t can be calculated hence C.

Hi,

Its C.

You need to calculate the distance, let that be D.

Now from 1 you just get the speed. To know D you need time and speed both. so 1 is insufficient

Using 2 you just get the difference in speed and the time, again no concrete values. so 2 is insufficient.

However if you combine 1 and 2 you get 2 speeds and the difference in time.

Here is how the solution would be

Earlier speed = 72.
time taken at 72 km/hr = t1
t1 = D/72


Later speed = 72+8 = 80 km/hr
Time taken at 80 km/hr = t2
t2 = D/80

Now t1-t2 = 1

D/72 -D/80 = 1

Solve this and you get D = 720 km.

C after 3:40 minutes

Let distance from her house to her parents house = D, average speed v, and time taken be t

(1) is insufficient, we only have t = D/72


From (2), D/(v+8) = D/v - 1

So this is not sufficient either, but if we combine (1) and (2), v = 72 and hence we can find out both. So the answer is C.
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basically, we are provided with two equations in 1statement 1 and 2.
having two equations it is possible to solve equality with two uknowns.

hence it is C.

30 seconds.
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let time req. be t.
let distance covered be d.

1.
d/t=72.
Insufficient

2.
d/(t-1)=80
Insufficient

1+2
d=72t
d=80(t-1)
72t=80(t-1)
Sufficient

Could you also solve this problem by thinking of it as a ratio? One of MGMAT's strategies for DS ratio questions is that if a DS question asks for the concrete value of one element of a ratio, you will need both the concrete value of another element and the relative value of 2 elements of the ratio. When you combine the two statements, you get a concrete value from statement 1 and two relative values from statement 2. Is that a logical way to solve this problem, once you already know that the two statements individually are insufficient?
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How many hours did it take Helen to drive from her house to her parents house?

1) Helen’s average speed on this trip was 72 kilometers per hour.
We know nothing about distance. If the distance was 72km then it would have taken one hour. If the distance was 720km then it would have taken 10 hours, etc. All we know is r=72
INSUFFICIENT

2) If Helen’s average speed on this trip had been 8 kilometers per hour greater, it would have taken her 1 hour less.
Time=distance/speed
T-1 = d/(s+8)
This does not provide enough information to solve for the question.
INSUFFICIENT

1+2) average speed (r) = 72, t-1 = d/(s+8)
t-1 = d/(72+8)
t-1 = d/80
This is where it gets tricky. At first I said that this isn't enough information to solve so I put down (E). However, d=r*t. If I plug in for d then I can cancel out t leaving r.
t-1 = r*t/(72+8)
t-1 = 72*t/(80)
80t-80 = 72t
8t = 80
t=10

A couple things to remember:
- If in doubt and unable to solve, try and substitute in a formula (like=r*t) to cancel out variables.
- remember to plug in any applicable numbers for all variables. For example, after plugging in r*t for d, I forgot to plug in 72 for r*t.
SUFFICIENT

(C)

Well, I thought that we were provided with 3 equations and 3 variables. The answer is the same (C) but I think my reasoning is slightly different.

Question stem: RT = D (3 variables, 1 equation). We need 2 more equations in the statements to solve this problem. Remember, whenever you are dealing with distance, you already have an equation (RT = D). The same goes for Work Problems (RT = W)

St 1: R = 72. Insufficient. St 1 just gives us 1 more equation.

St. 2: (R + 8)(T - 1) = D. Insufficient. St 2 just gives us 1 more equation.

St 1 + 2: we now have 2 more equations apart from the one given in the question stem. We now have 3 equations and 3 unknowns. We can solve for this stuff: no need to do the calculations.

Hope it makes sense.

First, write what we are solving for: "T?"

(1) R = 72 ---> Insufficient (We would also need the distance to solve for time ---> Using D=RT, we could get T = \(\frac{D}{R}\) =\(\frac{D}{72}\), but we have 2 variables and one equation)

(2) We translate the "If..." statement, saying the hypothetical distance is equal to the actual distance:
RT = (R+8)(T-1)
Again, 2 variables and 1 equation ---> Insufficient

(1) & (2) Together: Now, we have 2 variables and 2 equations --> Sufficient ---> Answer is C
(or, once you plug in R = 72 into statement 2, we just have one linear equation and one variable)


For another similar example of this "If..." wording, try this one: https://gmatclub.com/forum/a-store-curr ... l#p1161554
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distance = rate * time

(1) Helen's average speed on this trip was 72 kilometers per hour

distance = 72 * time

Without the distance we are not able to determine the time. Insufficient.

(2) If Helen's average speed on this trip had been 8 kilometers per hour greater , it would have taken her 1 hour less.

(r + 8)(t - 1) = distance

Two variables and one equation. Insufficient.

(1&2) r = 72
80(t - 1) = rt
We can solve for t. Sufficient.

Answer is C.
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