**Converting Metric Units Word Problems :**

In this section, you will learn how to solve word problems step by step using conversions between different metric units.

**Problem 1 : **

David travels 60 kilometers in two hours. How many meters of distance will he cover in one minute ?

**Solution : **

Distance covered in 2 hours = 60 kilometers

Distance covered in 1 hour = 30 kilometers

We know that,

1 hour = 60 minutes

1 kilometer = 1000 meters

**Given : **David travels 60 kilometers in two hours

Then,

2 hours -----> 60 km

1 hour -----> (60/2) km

1 hour -----> 30 km

60 minutes -----> (30 ⋅ 1000) meters

60 minutes -----> 30000 meters

1 minute -----> (30000/60) meters

1 minute -----> 500 meters

So, 500 meters of distance covered in 1 minute.

**Problem 2 : **

Mark jogged 15840 meters in 45 minutes. Find the speed of Mark in meter per minute.

**Solution : **

Speed = Distance / Time

Speed = 15840/45

Speed = 352 meters per minute

So, the speed of Mark is 352 meters per minute.

**Problem 3 : **

Use a fraction to find the length in meters of a tile that is 9 centimeters long.

**Solution : **

**Here, we convert smaller unit (centimeters) into bigger unit (meters). **

**So we have to divide.**

Because divide, we have to use the fraction 1/100.

We know that,

1 meter = 100 centimeters

Then,

9 centimeters = (9 ⋅ 1/100) meters

9 centimeters = 9/100 meters

So, 9 centimeters is equal to 9/100 meters.

**Problem 4 : **

Kevin has a pole that is 24 meters tall. If Kevin sets the pole on a 300 centimeters stand, how far from the floor will the top of the pole be (in meters) ?

**Solution : **

**Height of the pole = 24 meters**

**Height of the stand = 300 cm = (300/100) m = 3 m**

**Distance from the floor to the top of the pole is **

**= Height of the stand + Height of the pole**

**= 30 + 3 **

**= 33 meters**

So, the top of the pole is 33 meters far from the floor.

**Problem 5 : **

Becky and Keith each ran for exactly 20 minutes on a treadmill. Keith’s treadmill said he had run 18500 meters. Becky’s treadmill said she had run 2 kilometers. Who ran farther, and how much farther ?

**Solution : **

**Both Becky and Keith took the same amount of time. **

**That is 20 minutes.**

**Distance covered by Becky and Keith are given in different units. (Meters and Kilometers)**

**We have to make the units same. **

**Convert meters in to kilometers. **

**Then, **

**10000 m = (18500/1000) m = 18.5 km **

**Therefore,**

**Distance covered by Becky = 18.5 km -----(1) **

**Distance covered by Keith = 2 km ****-----(2)**

**Difference between (1) and (2) is **

**= 2 - 18.5**

**= 1.5 km**

So, Becky ran farther by 1.5 km.

**Problem 6 : **

David prepares 24 kilograms of metal in 1 hour 36 minutes. At the same rate, How many grams of metal will he prepare in one minute ?

**Solution : **

1 hr 36 min = 60 min + 36 min = 96 min

1 kg = 1000 grams

24 kg = 24 ⋅ 1000 grams = 24000 grams

**Given : **David prepares 24 kilograms of metal in 1 hour 36 minutes.

Then,

1 hr 36 min -----> 24 kg

96 min -----> 24000 grams

1 min -----> (24000/96) grams

1 min -----> 250 grams

So, David will prepare 200 grams of metal in one minute.

**Problem 7 : **

Mark used 15840 grams of metal to make an alloy in 45 minutes. Find the amount metal used in one minute (in grams).

**Solution : **

Metal used in 45 minutes = 15840 grams

Metal used in 1 minute = (15840/45) grams

Metal used in 1 minute = 352 grams

So, 352 grams of metal is used in 1 minute.

**Problem 8 : **

Mrs. Moore handed out 40 grams of almonds to each of her 22 students . How many dekagrams of almonds did Mrs. Moore hand out ?

**Solution : **

**Total no. of grams of almonds handed out is **

**= 4 **⋅** 22**

**= 88**

**Here, we convert smaller unit (grams) into bigger unit (deagrams).**

**So we have to divide.**

**We now that, **

**1 dekagram = 10 grams**

**Then, the total no. of dekagrams of almonds handed out is**

**= 88/10**

**= 8.8**

So, Mrs. Moore handed out 8.8 dekagrams of almonds.

**Problem 9 : **

Tommy uses 40 grams of cheese in each pizza he makes. How many kilograms of cheese does Tommy need to make 28 pizzas ?

**Solution : **

**Given : **Tommy uses 40 grams of cheese in each pizza he makes.

1 pizza -----> 40 grams of cheese

28 pizzas -----> 28 ⋅ 40 grams of cheese

28 pizzas ------> 1120 grams of cheese

28 pizzas ------> (1120/1000) kilograms of cheese

28 pizzas ------> 1.12 kilograms

So, Tommy needs 1.12 kilograms of cheese to make 28 pizzas.

**Problem 10 : **

A standard elevator in a mid rise building can hold a maximum weight of about 500 kilograms. Assuming an average adult weight of 70 kilograms, what is the maximum number of adults who could safely ride the elevator ?

**Solution : **

**Given :** Elevator can hold 500 kilograms.

If the average weight of an adult is **70 kilograms, then m****aximum no. of adults could safely ride the elevator is**

= 500/70

= 7.14

≈ 7

So, maximum number of adults who could safely ride the elevator is 7.

After having gone through the problems explained above, we hope that the students would have understood how to solve word problems using conversions between different metric units.

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