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# Laura and Jeff plan to drive along the same route to the same destinat

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Math Expert
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Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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16 Apr 2018, 05:52
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Difficulty:

45% (medium)

Question Stats:

72% (01:22) correct 28% (01:11) wrong based on 129 sessions

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Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?

A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes

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Re: Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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16 Apr 2018, 06:19
I think the right answer is C = 40 min,
Coz, the distance travelled by Jeff and Laura is the same , D = Vj*Tj (where Vj and Tj are velocity of Jeff and Time taken by Jeff)
and for Laura, D = Vl*Tl (where vl is velocity of laura, Tl is time taken by laura)
in the question it is mentioned that, Vl = 1.5 Vj
So, by equating above distance equations
D=D ==> Vj*Tj = Vl*Tl => Vj*1= 1.5 Vj*Tl => Tl = 1/1.5*60 = 40 min (Option C)
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Re: Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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16 Apr 2018, 06:33
Bunuel wrote:
Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?

A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes

------Laura ----Jeff
S-------1--------1--
V-----1+0.5-----1--
T-------?--------1--

T(?) = 1/ (1+0.5) = 2/3 *60 min= 40 min . Answer(C)
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Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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16 Apr 2018, 13:42
Bunuel wrote:
Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?

A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes

Assign a value

Jeff and Laura travel the same distance, D
We have
• a time for Jeff
• a rate for Laura in relation to Jeff

Given any distance, D, variable or assigned, we can
• find Jeff's rate and thus Laura's rate, and
• find Laura's time

Let D = 4 miles

• Jeff's rate? Jeff drives D = 4 miles in t = 1 hour
J's rate: $$\frac{D}{t}=\frac{4}{1}$$= 4 mph

• L's rate, 50% faster than J's = $$(1.5 * 4)=6$$ mph

• L's time? $$T=\frac{D}{r}=\frac{4}{6}=\frac{2}{3}$$ hour

L's time = 40 minutes

ANY fraction of an hour * 60 = minutes. So
$$\frac{2}{3}*60=40$$mins)

Algebra (or inverse proportion)
Let Jeff's rate = $$J$$
Let Laura's time = $$t_2$$
Jeff's time in minutes: 1 hour = $$60$$

• Overall strategy: Use equal distance to find Laura's time

1) Find distance in terms of Jeff, D = r*t

Jeff drives at rate $$J$$ mph for 60 minutes
D in terms of Jeff = $$(r*t)=(J*60)= 60J$$

2) Find distance in terms of Laura, D = r*t

Laura's rate? She drives 50% faster than Jeff
L's rate: $$(J+\frac{1}{2}J)=\frac{3}{2}J$$

L's time = $$t_2$$

D in terms of Laura = $$(r*t)=(\frac{3}{2}J*t_2)$$

3) D = D. Set distances equal, solve for Laura's time

$$\frac{3}{2}J * t_2 = 60J$$

So $$t_2 =\frac{60J}{(\frac{3}{2})J}=(60J*\frac{2}{3}J)=40$$
minutes

Laura's time, $$t_2 = 40$$ minutes

*Note: rate and time are inversely proportional. Distances are equal.
Flip Laura's rate, $$\frac{3}{2}J$$,
to get Laura's time, namely, $$\frac{2}{3}J$$.
If J's time is in hours, convert L's final time to minutes. Much quicker, though perhaps not as easy to see.

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Re: Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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17 Apr 2018, 16:13
Bunuel wrote:
Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?

A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes

Since Laura’s rate is 50% faster, or 3/2 of Joe’s rate, her time is 2/3 of Joe’s time. If it takes Joe 1 hour, it takes Laura 2/3 of an hour, or 40 minutes.

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Re: Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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17 Apr 2018, 19:47
Bunuel wrote:
Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?

A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes

If Laura travels at 150%, or 3/2, of Jeff's rate,
it will take her, inversely, 2/3 of Jeff's time
2/3*60 minutes=40 minutes
C
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Re: Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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30 Apr 2018, 09:23
Let's understand it in simple way
Suppose Jeff travel 1 km in 1 hr

As per question 50% faster means Laura will travel 1.5 km in 1 hr
Means she will travel 1 km in 1/1.5 hr
i.e 10/15 hr

10*60/15 min
=40 min

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Re: Laura and Jeff plan to drive along the same route to the same destinat  [#permalink]

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30 Apr 2018, 13:06
2
Bunuel wrote:
Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?

A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes

Let's assume that distance is 1 km and jeff's speed is 1 km/hr

Laura's speed is 50% faster than jeff's, hence Laura's speed is 1.5 km/hr

time traken = distance / speed = 1/1.5 = 10 /15 * 60 minutes = 40 minutes (C)
Re: Laura and Jeff plan to drive along the same route to the same destinat &nbs [#permalink] 30 Apr 2018, 13:06
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