# Math Help - rate

1. ## rate

Whats the easiest and most simplest way to understand and work out this solution. Please show any shortcuts. Thanks

A.Ben sails 1/3 of his trip at 4km/h, the next 1/3 at 8 km/h and the last 1/3 at 6 km/h. The trip takes him 9 hours and 45 minutes. How far was the complete trip ?

B.In a zoo there are 17 more monkeys than lions and 30 more lizards than lions. If there were 151 animals in total, how many of each animal are there ?

Thanks

2. Originally Posted by chhoeuk

Whats the easiest and most simplest way to understand and work out this solution. Please show any shortcuts. Thanks

A.Ben sails 1/3 of his trip at 4km/h, the next 1/3 at 8 km/h and the last 1/3 at 6 km/h. The trip takes him 9 hours and 45 minutes. How far was the complete trip ?
Note: 9 hours 45 mins is 39/4 hours.

Recall that $\mbox { Speed } = \frac { \mbox { Distance }}{ \mbox { Time }}$

$\Rightarrow \mbox { Time } = \frac { \mbox { Distance }}{ \mbox { Speed }}$

Let $D$ be the total distance traveled
Let $t_1$ be the time for the first part of the journey
Let $t_2$ be the time for the second part of the journey
Let $t_3$ be the time for the last part of the journey

For the first third of the trip we travel $\frac {1}{3} D$:

$t_1 = \frac {distance}{time} = \frac { \frac {D}{3}}{4} = \frac {D}{12}$

For the second part of the journey, we also travel $\frac {1}{3} D$:

$t_2 = \frac {distance}{speed} = \frac { \frac {D}{3}}{8} = \frac {D}{24}$

For the last part of the trip, we also travel $\frac {1}{3} D$:

$t_3 = \frac {distance}{speed} = \frac { \frac {D}{3}}{6} = \frac {D}{18}$

Now all these times must add up to $\frac {39}{4}$ hours.

So we have:

$t_1 + t_2 + t_3 = \frac {39}{4}$

$\Rightarrow \frac {D}{12} + \frac {D}{24} + \frac {D}{18} = \frac {39}{4}$

solving for $D$ we get: $\boxed { D = 54 \mbox { km } }$

3. Originally Posted by chhoeuk

B.In a zoo there are 17 more monkeys than lions and 30 more lizards than lions. If there were 151 animals in total, how many of each animal are there ?
i think there's something wrong with this question...but maybe i'm too sleepy. i'm going to bed. good luck

4. Jhevon says it's wrong because after solving for it, he probably gets a number and two thirds lions, which clearly cannot be in this time and in this world... unless we define a third of a lion as a cat, a third of a monkey as Taco Bell's chihuahua, and a third of a lizard as its head. Also, why does the zoo only have three types of animals? In any case, my house is much more of a zoo than that. We have: cats, dogs, lizards, cockroaches, different colored ants, birds, a smurf, and an orange snork to name a few... but no lions or monkeys. Maybe I should open a zoo.

What I mean is please check for typos either in the numbers or in the animals.

5. Originally Posted by chhoeuk

B.In a zoo there are 17 more monkeys than lions and 30 more lizards than lions. If there were 151 animals in total, how many of each animal are there ?

Thanks

L= lions
M= monkey
and Z= Lizards

M=L+17
Z=L+30

M+L+Z = 151

(L+17)+L+(L+30) = 151
M Z

3L+47= 151

3L = 104
L = 34.6666666666666666 and it's kind hard to have only part of an animal.