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

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)

Answer C

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

• 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

Answer C

*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.

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.

Answer: C

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

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

Posted from my mobile device

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)

Let the Jeff's speed be 1 mph
So Laura speed will be =1.5 mph
Laura travel: 1.5 miles--60 mins
1 miles= 60/1.5= 40 mins

Ans(C)

Formula: D = RT (Distance equals Rate x Time)

Given:

1. Jeff's traveling time: T = 1 hour, or 60 minutes (since the answer bank has time in minutes)
2. Jeff's rate: R = r
3. Laura's rate: \(1.5r, or \frac{3}{2} * r\)

Solve: Sine D = RT and their distance traveled is the same (traveling to same destination), we can do the following:

1. Jeff: D = 60r (since I converted 1 hour to minutes)
2. Laura: \(D = \frac{3}{2} * r\)
3. Using both equations, we get: \(60r = \frac{3T}{2} * r\)
4. Cancel out both rates, and solve for T: \(T = 60 * \frac{2}{3} = 40 minutes\)

let distance = 10 kms
so for Jeff time ; 1 hr
speed ; 10kmph
speed of Laura ; 15 kmph
so time for Laura to cover 10 kms ; 10/15 ; 2/3*60 ; 40 mins
IMO C

Given: Laura and Jeff plan to drive along the same route to the same destination.

Asked: 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?

Distance = v * 1 hours = 1.5 v * t
t = 1/1.5 = 2/3 hours = 40 mins

IMO C

D/V=T=60 mins, while V'=1.5V, D/V'=D/(1.5V)=(2/3)(D/V)=(2/3)(60mins)=40 mins.

As always on rates questions, I find it easiest (and with the lowest risk of making a silly mistake!) to just plug in. In this case, there's no variable, but there's something that would be really helpful to know: how far they travel. So let's just make it up. With mph questions, my brain finds it easiest to use something like 60 or 30. Let's do 60.

It takes Jeff 1 hour and he goes 60 miles, so he travels at 60mph.
Laura travels 50% faster, so 90mph. It takes her 60/90 = 2/3rds of an hour.
Answer choice C.

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